diff --git a/moto/secretsmanager/exceptions.py b/moto/secretsmanager/exceptions.py
index d4563dc4..7ef1a923 100644
--- a/moto/secretsmanager/exceptions.py
+++ b/moto/secretsmanager/exceptions.py
@@ -15,6 +15,7 @@ class ResourceNotFoundException(SecretsManagerClientError):
         )
 
 
+# Using specialised exception due to the use of a non-ASCII character
 class SecretNotFoundException(SecretsManagerClientError):
     def __init__(self):
         self.code = 404
@@ -24,6 +25,17 @@ class SecretNotFoundException(SecretsManagerClientError):
         )
 
 
+# Using specialised exception due to the use of a non-ASCII character
+class SecretHasNoValueException(SecretsManagerClientError):
+    def __init__(self, version_stage):
+        self.code = 404
+        super(SecretHasNoValueException, self).__init__(
+            "ResourceNotFoundException",
+            message=u"Secrets Manager can\u2019t find the specified secret "
+                    u"value for staging label: {}".format(version_stage)
+        )
+
+
 class ClientError(SecretsManagerClientError):
     def __init__(self, message):
         super(ClientError, self).__init__(
diff --git a/moto/secretsmanager/models.py b/moto/secretsmanager/models.py
index 1e9d6a51..e1a380c3 100644
--- a/moto/secretsmanager/models.py
+++ b/moto/secretsmanager/models.py
@@ -10,8 +10,8 @@ import boto3
 
 from moto.core import BaseBackend, BaseModel
 from .exceptions import (
-    ResourceNotFoundException,
     SecretNotFoundException,
+    SecretHasNoValueException,
     InvalidParameterException,
     ResourceExistsException,
     InvalidRequestException,
@@ -87,10 +87,7 @@ class SecretsManagerBackend(BaseBackend):
             response_data["SecretBinary"] = secret_version['secret_binary']
 
         if 'secret_string' not in secret_version and 'secret_binary' not in secret_version:
-            raise ResourceNotFoundException(
-                u"Secrets Manager can\u2019t find the specified secret value for staging label: %s" %
-                (version_stage or u"AWSCURRENT")
-            )
+            raise SecretHasNoValueException(version_stage or u"AWSCURRENT")
 
         response = json.dumps(response_data)