Though we were unable to find this app from Blizzard directly, we believe it to be legitimate. However, we have contacted Blizzard for confirmation. We'll let you know what they have to say when we hear back from them. Update: Here is the link to the official Blizzard support page for the Android app. Looks like it's legit. Update 2: Here is the official announcement.
If you don't have an Authenticator yet, we can't recommend it enough. The added protection an authenticator provides to your account is much greater than the slight inconvenience of needing access to your phone whenever you login. This is particularly the case if you game at internet cafes.
Gallery: Battle.net Mobile Authenticator