diff --git a/.changelog/39067.txt b/.changelog/39067.txt
new file mode 100644
index 00000000000..be2d8804fd3
--- /dev/null
+++ b/.changelog/39067.txt
@@ -0,0 +1,3 @@
+```release-note:bug
+resource/aws_ssm_parameter: Fix `ValidationException: Parameter ARN is not supported for this operation` errors when deleting resources imported by ARN
+```
\ No newline at end of file
diff --git a/internal/service/ssm/parameter.go b/internal/service/ssm/parameter.go
index 082353da5e2..a5fe04fa270 100644
--- a/internal/service/ssm/parameter.go
+++ b/internal/service/ssm/parameter.go
@@ -337,7 +337,8 @@ func resourceParameterDelete(ctx context.Context, d *schema.ResourceData, meta i
 
 	log.Printf("[DEBUG] Deleting SSM Parameter: %s", d.Id())
 	_, err := conn.DeleteParameter(ctx, &ssm.DeleteParameterInput{
-		Name: aws.String(d.Id()),
+		// Use "name" instead of "id" in case the resource was imported by ARN.
+		Name: aws.String(d.Get(names.AttrName).(string)),
 	})
 
 	if errs.IsA[*awstypes.ParameterNotFound](err) {
diff --git a/internal/service/ssm/parameter_test.go b/internal/service/ssm/parameter_test.go
index ee8616e558d..57a8117cf3d 100644
--- a/internal/service/ssm/parameter_test.go
+++ b/internal/service/ssm/parameter_test.go
@@ -1053,6 +1053,41 @@ func TestAccSSMParameter_Secure_keyUpdate(t *testing.T) {
 	})
 }
 
+// lintignore:AT002
+func TestAccSSMParameter_importByARN(t *testing.T) {
+	ctx := acctest.Context(t)
+	var param awstypes.Parameter
+	name := fmt.Sprintf("%s_%s", t.Name(), sdkacctest.RandString(10))
+	resourceName := "aws_ssm_parameter.test"
+
+	resource.ParallelTest(t, resource.TestCase{
+		PreCheck:                 func() { acctest.PreCheck(ctx, t) },
+		ErrorCheck:               acctest.ErrorCheck(t, names.SSMServiceID),
+		ProtoV5ProviderFactories: acctest.ProtoV5ProviderFactories,
+		CheckDestroy:             testAccCheckParameterDestroy(ctx),
+		Steps: []resource.TestStep{
+			{
+				Config: testAccParameterConfig_basic(name, "String", "test2"),
+				Check: resource.ComposeTestCheckFunc(
+					testAccCheckParameterExists(ctx, resourceName, &param),
+				),
+			},
+			// Test import by ARN.
+			// https://github.com/hashicorp/terraform-provider-aws/issues/39050.
+			{
+				ResourceName: resourceName,
+				ImportState:  true,
+				ImportStateIdFunc: func(*terraform.State) (string, error) {
+					return aws.ToString(param.ARN), nil
+				},
+				ImportStateVerify:                    true,
+				ImportStateVerifyIdentifierAttribute: names.AttrName,
+				ImportStateVerifyIgnore:              []string{names.AttrID, "overwrite"},
+			},
+		},
+	})
+}
+
 func testAccCheckParameterRecreated(t *testing.T, before, after *awstypes.Parameter) resource.TestCheckFunc {
 	return func(s *terraform.State) error {
 		if *before.Name == *after.Name {