An image of Abdulah Husseini buying cans of beers went viral when social media users pointed out his likeness to the sitcom actor.
The 36-year-old had used a stolen bank card to make the purchase after swiping a wallet from a man's jacket at an all-you-can-eat buffet.
The thief used the card to make or attempt to make fraudulent purchases at four shops in Blackpool, Lancashire, last September.
When police in Blackpool posted a CCTV image of Husseini buying beer at an Iceland store in an attempt to track him down, the post quickly amassed more than 11 million shares - even attracting the attention of Schwimmer himself.
The actor shared a video of himself scurrying through a convenience store carrying a carton of beer and looking suspicious.
He captioned the video: "Officers, I swear it wasn't me. As you can see, I was in New York.