Shemar Moore says the woman who showed up at his home with luggage after being duped by a catfish almost got into a catfight with the real woman in his life … because his significant other was ready to protect her territory … by any means necessary!!!

We got the “S.W.AT.” star in New York City on Tuesday, and he told our photog Jesiree Dizon was ready to throw down when a woman they didn’t know rolled up to their pad ready to move in.

Shemar says Jesiree had her boxing gloves ready … but he actually feels bad for the woman, telling us she got catfished and conned into believing he wanted her to live with him.

He said that even though they called the cops, the woman wasn’t arrested and was treated with respect.

And get this … Shemar tells us this isn’t even the first time this has happened.