Here is video of the man suspected of stealing Tom Brady's Super Bowl jersey ... according to FS1 ... and it sure looks like he's got something under his arm.

The suspect was captured on video by FOX, the network that aired Super Bowl 51 -- and while his face is blurred, you can see his tie is terrible.

We are told the frame that shows the suspect clutching an item under his arm is what blew the case wide open for authorities.