diff --git a/moto/secretsmanager/models.py b/moto/secretsmanager/models.py
index 6f9a00b0e..7bd38259a 100644
--- a/moto/secretsmanager/models.py
+++ b/moto/secretsmanager/models.py
@@ -44,7 +44,15 @@ class SecretsManagerBackend(BaseBackend):
         return (dt - epoch).total_seconds()
 
     def get_secret_value(self, secret_id, version_id, version_stage):
-
+        # can fetch by both arn and by name
+        # but we are storing via name
+        # so we need to change the arn to name
+        # if it starts with arn then the secret id is arn
+        if secret_id.startswith("arn:aws:secretsmanager:%s" % self.region):
+            # split the arn by colon
+            # then get the last value which is the name appended with a random string
+            # then remove the random string
+            secret_id = '-'.join(secret_id.split(':')[-1].split('-')[:-1])
         if not self._is_valid_identifier(secret_id):
             raise SecretNotFoundException()
 
diff --git a/tests/test_secretsmanager/test_secretsmanager.py b/tests/test_secretsmanager/test_secretsmanager.py
index a7c7a6862..cc64dc874 100644
--- a/tests/test_secretsmanager/test_secretsmanager.py
+++ b/tests/test_secretsmanager/test_secretsmanager.py
@@ -26,6 +26,18 @@ def test_get_secret_value():
     assert result["SecretString"] == "foosecret"
 
 
+@mock_secretsmanager
+def test_get_secret_value_by_arn():
+    conn = boto3.client("secretsmanager", region_name="us-west-2")
+
+    secret_value = "test_get_secret_value_by_arn"
+    result = conn.create_secret(
+        Name="java-util-test-password", SecretString=secret_value
+    )
+    result = conn.get_secret_value(SecretId=result["ARN"])
+    assert result["SecretString"] == secret_value
+
+
 @mock_secretsmanager
 def test_get_secret_value_binary():
     conn = boto3.client("secretsmanager", region_name="us-west-2")