Model Danii Banks says she got a rude awakening when an alleged armed robber busted into her pad demanding money, while she stood startled … and totally in the buff.

This surveillance shows the naked truth, according to Danii, who tells us she was asleep in her Chamblee, GA apartment last week when she heard a loud noise, prompting her dogs to bark like crazy. You can see in the footage … the alleged robber was armed with a gun and demanding money.

Danii stumbled into the room, naked and seeming totally out of it.

Danii — an IG model with more than 2.5 million followers — says the crook made her open a safe, which she says was empty. Danii adds the man then pushed her onto the bed before he fled.

According to the Chamblee PD … cops were dispatched to an armed robbery call to her apartment where cops say they found Danii hysterical and crying because she told them someone tried robbing her at gunpoint.

Cops say they observed a street-side door to her apartment was damaged from being forced open. Danii says she told cops the man was a light-skinned black male.

No arrests have been made, but cops have Danii’s surveillance footage and are still investigating.