Nicki Minaj -- Big Fight At Minaj's House Over Maid

There was a big confrontation at Nicki Minaj's house in Hollywood moments ago ... and it got so bad the cops came ... TMZ has learned.

Here's the backstory. Law enforcement tells us, a couple of weeks ago, Nicki's maid took a photo of the singer out of the trash and then asked Nicki to sign it. Nicki got pissed and fired her.

Cops tell us, the maid did come back today, and Nicki became enraged and ordered her to leave. A source privy to the fight tells TMZ, the maid stood her ground, demanding not to be "treated like an animal" -- at which point, Nicki allegedly said, "I'll show you how to treat someone like an animal ... get the f**k out of my house!"

Now here's where the stories are a bit conflicting. One source says -- contrary to what the cops say -- Nicki actually made a mistake, saw another maid and assumed she was the one Nicki had fired.

We have had multiple people involved in the incident tell us ... the maid Nicki confronted was NOT the same maid she fired a few weeks ago. It was a case of mistaken identity.

Either way, Nicki's boyfriend got in the act and began pushing the maid with his body. The maid's boss called the cops and filed a battery report.