J.Lo is angry over a story that originated in a German tabloid ... in which the maid says she tried to approach the singer's assistants while they were staying at a fancy German hotel last month and asked for Jennifer's signature. The maid claims the singer complained to management and she was fired the next day.

Now, Lopez lashing back ... saying, "C'mon thought you knew me better than this.. Would never get anyone fired over an autograph."

Sources close to Lopez tell TMZ ... there WAS an incident involving a maid, but it didn't involve an autograph. We're told the maid had "barged" into the room unannounced ... and the singer's security immediately removed the maid from the room out of concern for the singer's safety.

We're told hotel management has since assured Lopez's people that no one was fired -- but the maid company the hotel uses has relocated the maid in question to a different property.