The image features a man with dark bushy hair, holding a pack of beer, staring up at the camera.
The original post read: "Do you recognise this man? We want to speak to him in relation to a theft at a Blackpool restaurant on the 20th September."
However, Facebook users were quick to point out the similarities with the US actor.
One person quoted the famous theme tune by the Rembrandts: "So no-one told me life was going to be this wayyyy."
Another said: "I heard his getaway driver was stuck in second gear..."
Nick Croston said: "I don't think it's been this guy's day, his week, his month or even his year...."
Scottish police also got in on the act, with officers in Dumfries and Galloway also sharing the post and warning members of the public to 'keep away' from the suspect.
"He is known to have studied karate and we believe he has mastered the art of Unagi, the state of total awareness," they said, in a reference to one episode of the sitcom where Ross claims to be an expert in self-defence.
Even the Blackpool Police joined in on the joke.
"Thank you to everyone for your speedy responses. We have investigated this matter thoroughly and have confirmed that David Schwimmer was in America on this date. We're so sorry it has to be this way."