There does not seem to be consensus on this. For example, Under the Software Requirements section, MongoDB, is the following quote: "The MongoDB databases backing MMS must be MongoDB 2.4.9 or later. The MongoDB replica sets and sharded clusters to be backed up must be running MongoDB 2.4.3 or later."

Also:

https://jira.mongodb.org/secure/attachment/34148/backup-manual.txt

DOCS-1527 says it will work for all replica sets >= 2.0 and sharded clusters >= 2.4.3

https://jira.mongodb.org/browse/DOCS-1527

This FAQ says it works for all replica sets >= 2.2 and sharded clusters >= 2.4.3

http://mms.mongodb.com/help/faq/backup/

According to Cailin it should be >= 2.2 for replica sets and >= 2.4.3 for sharded clusters.