diff --git a/packages/babel-preset-env/package.json b/packages/babel-preset-env/package.json
index 15a72e4cb3..b9a54adfc3 100644
--- a/packages/babel-preset-env/package.json
+++ b/packages/babel-preset-env/package.json
@@ -61,7 +61,7 @@
     "@babel/plugin-transform-unicode-regex": "^7.7.4",
     "@babel/types": "^7.7.4",
     "browserslist": "^4.6.0",
-    "core-js-compat": "^3.4.7",
+    "core-js-compat": "^3.6.0",
     "invariant": "^2.2.2",
     "js-levenshtein": "^1.1.3",
     "semver": "^5.5.0"
diff --git a/packages/babel-preset-env/test/fixtures/corejs3/entry-ie-11/output.mjs b/packages/babel-preset-env/test/fixtures/corejs3/entry-ie-11/output.mjs
index f6b2431273..26b355d9cb 100644
--- a/packages/babel-preset-env/test/fixtures/corejs3/entry-ie-11/output.mjs
+++ b/packages/babel-preset-env/test/fixtures/corejs3/entry-ie-11/output.mjs
@@ -103,6 +103,7 @@ import "core-js/modules/es.reflect.prevent-extensions";
 import "core-js/modules/es.reflect.set";
 import "core-js/modules/es.reflect.set-prototype-of";
 import "core-js/modules/es.regexp.constructor";
+import "core-js/modules/es.regexp.exec";
 import "core-js/modules/es.regexp.flags";
 import "core-js/modules/es.regexp.to-string";
 import "core-js/modules/es.set";
diff --git a/packages/babel-preset-env/test/fixtures/corejs3/entry-ie-9/output.mjs b/packages/babel-preset-env/test/fixtures/corejs3/entry-ie-9/output.mjs
index 80f642659b..6c47ffc5a7 100644
--- a/packages/babel-preset-env/test/fixtures/corejs3/entry-ie-9/output.mjs
+++ b/packages/babel-preset-env/test/fixtures/corejs3/entry-ie-9/output.mjs
@@ -107,6 +107,7 @@ import "core-js/modules/es.reflect.prevent-extensions";
 import "core-js/modules/es.reflect.set";
 import "core-js/modules/es.reflect.set-prototype-of";
 import "core-js/modules/es.regexp.constructor";
+import "core-js/modules/es.regexp.exec";
 import "core-js/modules/es.regexp.flags";
 import "core-js/modules/es.regexp.to-string";
 import "core-js/modules/es.set";
diff --git a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-specific-targets/stdout.txt b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-specific-targets/stdout.txt
index 7db11b8352..548122b74e 100644
--- a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-specific-targets/stdout.txt
+++ b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-specific-targets/stdout.txt
@@ -174,7 +174,7 @@ Using polyfills with `entry` option:
   es.reflect.set { "edge":"13", "ie":"10", "ios":"9", "safari":"7" }
   es.reflect.set-prototype-of { "ie":"10", "ios":"9", "safari":"7" }
   es.regexp.constructor { "edge":"13", "ie":"10", "ios":"9", "safari":"7" }
-  es.regexp.exec { "safari":"7" }
+  es.regexp.exec { "ie":"10", "ios":"9", "safari":"7" }
   es.regexp.flags { "edge":"13", "ie":"10", "safari":"7" }
   es.regexp.to-string { "edge":"13", "ie":"10", "ios":"9", "safari":"7" }
   es.set { "edge":"13", "firefox":"49", "ie":"10", "ios":"9", "safari":"7" }
diff --git a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-decimals/stdout.txt b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-decimals/stdout.txt
index efcedad873..3b1bef7590 100644
--- a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-decimals/stdout.txt
+++ b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-decimals/stdout.txt
@@ -167,6 +167,7 @@ Using polyfills with `entry` option:
   es.reflect.set { "electron":"0.36", "ie":"10" }
   es.reflect.set-prototype-of { "electron":"0.36", "ie":"10" }
   es.regexp.constructor { "electron":"0.36", "ie":"10", "node":"6.1" }
+  es.regexp.exec { "ie":"10" }
   es.regexp.flags { "electron":"0.36", "ie":"10" }
   es.regexp.to-string { "electron":"0.36", "ie":"10" }
   es.set { "electron":"0.36", "ie":"10", "node":"6.1" }
diff --git a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings-minor-3.0/stdout.txt b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings-minor-3.0/stdout.txt
index af5f0f9ffe..e8694a81fd 100644
--- a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings-minor-3.0/stdout.txt
+++ b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings-minor-3.0/stdout.txt
@@ -154,6 +154,7 @@ Using polyfills with `entry` option:
   es.reflect.set { "ie":"10" }
   es.reflect.set-prototype-of { "ie":"10" }
   es.regexp.constructor { "ie":"10" }
+  es.regexp.exec { "ie":"10" }
   es.regexp.flags { "ie":"10" }
   es.regexp.to-string { "ie":"10" }
   es.set { "ie":"10" }
diff --git a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings-minor-3.1/stdout.txt b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings-minor-3.1/stdout.txt
index c74e3e37cb..e13d536c01 100644
--- a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings-minor-3.1/stdout.txt
+++ b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings-minor-3.1/stdout.txt
@@ -155,6 +155,7 @@ Using polyfills with `entry` option:
   es.reflect.set { "ie":"10" }
   es.reflect.set-prototype-of { "ie":"10" }
   es.regexp.constructor { "ie":"10" }
+  es.regexp.exec { "ie":"10" }
   es.regexp.flags { "ie":"10" }
   es.regexp.to-string { "ie":"10" }
   es.set { "ie":"10" }
diff --git a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings/stdout.txt b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings/stdout.txt
index caff30ef49..2ea0685394 100644
--- a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings/stdout.txt
+++ b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3-versions-strings/stdout.txt
@@ -154,6 +154,7 @@ Using polyfills with `entry` option:
   es.reflect.set { "ie":"10" }
   es.reflect.set-prototype-of { "ie":"10" }
   es.regexp.constructor { "ie":"10" }
+  es.regexp.exec { "ie":"10" }
   es.regexp.flags { "ie":"10" }
   es.regexp.to-string { "ie":"10" }
   es.set { "ie":"10" }
diff --git a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3/stdout.txt b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3/stdout.txt
index b337515f60..e27aade519 100644
--- a/packages/babel-preset-env/test/fixtures/debug/entry-corejs3/stdout.txt
+++ b/packages/babel-preset-env/test/fixtures/debug/entry-corejs3/stdout.txt
@@ -156,6 +156,7 @@ Using polyfills with `entry` option:
   es.reflect.set { "ie":"10" }
   es.reflect.set-prototype-of { "ie":"10" }
   es.regexp.constructor { "ie":"10", "node":"6" }
+  es.regexp.exec { "ie":"10" }
   es.regexp.flags { "ie":"10" }
   es.regexp.to-string { "ie":"10" }
   es.set { "ie":"10", "node":"6" }