diff --git a/CHANGELOG.md b/CHANGELOG.md
index f54f01397e32..b68bdb936a0b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,8 @@
 
 ### Features
 
+* `[jest-matcher-utils]` Change "suggest to equal" message to be more advisory
+  ([#6103](https://github.com/facebook/jest/issues/6103))
 * `[jest-message-util]` Don't ignore messages with `vendor` anymore
   ([#6117](https://github.com/facebook/jest/pull/6117))
 * `[jest-validate]` Get rid of `jest-config` dependency
diff --git a/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap b/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
index e77f3ee64c5a..711f01c60f77 100644
--- a/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
+++ b/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
@@ -290,7 +290,7 @@ Received: <red>[]</>
 
 Difference:
 
-<dim>Compared values have no visual difference.</> <dim>Looks like you wanted to test for object/array equality with the stricter \`toBe\` matcher. You probably need to use \`toEqual\` instead.</>"
+<dim>Compared values have no visual difference.</> <dim>Note that you are testing for equality with the stricter \`toBe\` matcher using \`Object.is\`. For deep equality only, use \`toEqual\` instead.</>"
 `;
 
 exports[`.toBe() fails for: {"a": 1} and {"a": 1} 1`] = `
@@ -301,7 +301,7 @@ Received: <red>{\\"a\\": 1}</>
 
 Difference:
 
-<dim>Compared values have no visual difference.</> <dim>Looks like you wanted to test for object/array equality with the stricter \`toBe\` matcher. You probably need to use \`toEqual\` instead.</>"
+<dim>Compared values have no visual difference.</> <dim>Note that you are testing for equality with the stricter \`toBe\` matcher using \`Object.is\`. For deep equality only, use \`toEqual\` instead.</>"
 `;
 
 exports[`.toBe() fails for: {"a": 1} and {"a": 5} 1`] = `
@@ -329,7 +329,7 @@ Received: <red>{}</>
 
 Difference:
 
-<dim>Compared values have no visual difference.</> <dim>Looks like you wanted to test for object/array equality with the stricter \`toBe\` matcher. You probably need to use \`toEqual\` instead.</>"
+<dim>Compared values have no visual difference.</> <dim>Note that you are testing for equality with the stricter \`toBe\` matcher using \`Object.is\`. For deep equality only, use \`toEqual\` instead.</>"
 `;
 
 exports[`.toBe() fails for: -0 and 0 1`] = `
diff --git a/packages/jest-matcher-utils/src/index.js b/packages/jest-matcher-utils/src/index.js
index 8123394744dc..232b0e33cba9 100644
--- a/packages/jest-matcher-utils/src/index.js
+++ b/packages/jest-matcher-utils/src/index.js
@@ -49,7 +49,7 @@ const NUMBERS = [
 ];
 
 export const SUGGEST_TO_EQUAL = chalk.dim(
-  'Looks like you wanted to test for object/array equality with the stricter `toBe` matcher. You probably need to use `toEqual` instead.',
+  'Note that you are testing for equality with the stricter `toBe` matcher using `Object.is`. For deep equality only, use `toEqual` instead.',
 );
 
 export const SUGGEST_TO_CONTAIN_EQUAL = chalk.dim(