diff --git a/aws/resource_aws_lambda_function_test.go b/aws/resource_aws_lambda_function_test.go
index 608e3b306edf..189b8543afbf 100644
--- a/aws/resource_aws_lambda_function_test.go
+++ b/aws/resource_aws_lambda_function_test.go
@@ -616,6 +616,39 @@ func TestAccAWSLambdaFunction_tracingConfig(t *testing.T) {
 	})
 }
 
+// This test is to verify the existing behavior in the Lambda API where the KMS Key ARN
+// is not returned if environment variables are not in use. If the API begins saving this
+// value and the kms_key_arn check begins failing, the documentation should be updated.
+// Reference: https://github.com/terraform-providers/terraform-provider-aws/issues/6366
+func TestAccAWSLambdaFunction_KmsKeyArn_NoEnvironmentVariables(t *testing.T) {
+	var function1 lambda.GetFunctionOutput
+
+	rName := acctest.RandomWithPrefix("tf-acc-test")
+	resourceName := "aws_lambda_function.test"
+
+	resource.ParallelTest(t, resource.TestCase{
+		PreCheck:     func() { testAccPreCheck(t) },
+		Providers:    testAccProviders,
+		CheckDestroy: testAccCheckLambdaFunctionDestroy,
+		Steps: []resource.TestStep{
+			{
+				Config: testAccAWSLambdaConfigKmsKeyArnNoEnvironmentVariables(rName),
+				Check: resource.ComposeTestCheckFunc(
+					testAccCheckAwsLambdaFunctionExists(resourceName, rName, &function1),
+					resource.TestCheckResourceAttr(resourceName, "kms_key_arn", ""),
+				),
+				ExpectNonEmptyPlan: true,
+			},
+			{
+				ResourceName:            resourceName,
+				ImportState:             true,
+				ImportStateVerify:       true,
+				ImportStateVerifyIgnore: []string{"filename", "publish"},
+			},
+		},
+	})
+}
+
 func TestAccAWSLambdaFunction_Layers(t *testing.T) {
 	var conf lambda.GetFunctionOutput
 
@@ -2192,6 +2225,42 @@ resource "aws_lambda_function" "test" {
 `, funcName)
 }
 
+func testAccAWSLambdaConfigKmsKeyArnNoEnvironmentVariables(rName string) string {
+	return fmt.Sprintf(baseAccAWSLambdaConfig(rName, rName, rName)+`
+resource "aws_kms_key" "test" {
+  description             = %[1]q
+  deletion_window_in_days = 7
+
+  policy = <<POLICY
+{
+  "Version": "2012-10-17",
+  "Id": "kms-tf-1",
+  "Statement": [
+    {
+      "Sid": "Enable IAM User Permissions",
+      "Effect": "Allow",
+      "Principal": {
+        "AWS": "*"
+      },
+      "Action": "kms:*",
+      "Resource": "*"
+    }
+  ]
+}
+POLICY
+}
+
+resource "aws_lambda_function" "test" {
+  filename      = "test-fixtures/lambdatest.zip"
+  function_name = %[1]q
+  handler       = "exports.example"
+  kms_key_arn   = "${aws_kms_key.test.arn}"
+  role          = "${aws_iam_role.iam_for_lambda.arn}"
+  runtime       = "nodejs8.10"
+}
+`, rName)
+}
+
 func testAccAWSLambdaConfigWithLayers(funcName, layerName, policyName, roleName, sgName string) string {
 	return fmt.Sprintf(baseAccAWSLambdaConfig(policyName, roleName, sgName)+`
 resource "aws_lambda_layer_version" "test" {
diff --git a/website/docs/r/lambda_function.html.markdown b/website/docs/r/lambda_function.html.markdown
index 8af55a4b3745..f62307eaa041 100644
--- a/website/docs/r/lambda_function.html.markdown
+++ b/website/docs/r/lambda_function.html.markdown
@@ -157,7 +157,7 @@ large files efficiently.
 * `publish` - (Optional) Whether to publish creation/change as new Lambda Function Version. Defaults to `false`.
 * `vpc_config` - (Optional) Provide this to allow your function to access your VPC. Fields documented below. See [Lambda in VPC][7]
 * `environment` - (Optional) The Lambda environment's configuration settings. Fields documented below.
-* `kms_key_arn` - (Optional) The ARN for the KMS encryption key.
+* `kms_key_arn` - (Optional) Amazon Resource Name (ARN) of the AWS Key Management Service (KMS) key that is used to encrypt environment variables. If this configuration is not provided when environment variables are in use, AWS Lambda uses a default service key. If this configuration is provided when environment variables are not in use, the AWS Lambda API does not save this configuration and Terraform will show a perpetual difference of adding the key. To fix the perpetual difference, remove this configuration.
 * `source_code_hash` - (Optional) Used to trigger updates. Must be set to a base64-encoded SHA256 hash of the package file specified with either `filename` or `s3_key`. The usual way to set this is `filebase64sha256("file.zip")` (Terraform 0.11.12 and later) or `base64sha256(file("file.zip"))` (Terraform 0.11.11 and earlier), where "file.zip" is the local filename of the lambda function source archive.
 * `tags` - (Optional) A mapping of tags to assign to the object.