A statement from the Balmoral Stadium side read: "Cove Rangers FC is aware of an image which is circulating relating to one of our players at the recent Celtic v Rangers match.
"As a club we do not condone such behaviour and expect all of our players to represent our club in the correct manner at all times.
"Fraser Aird's contract with the club was due to expire at the start of January and as a result he will be leaving the club with immediate effect."
The former Canada international was sitting with the visiting support at Celtic Park and appeared in pictures broadcast by Sky Sports following the final whistle.
Numerous fans highlighted the player's appearance, with one tweeting a video clip with the caption: "Nae way is that Fraser Aird hahaha" while another viewer added: "Fraser Aird at the end giving it big licks, glad he doesn't play for my club any more - embarrassing."
Toronto-born Aird, 24, started his career with Rangers and represented the club between 2012 and 2017, scoring 12 goals in 85 appearances.
He spent time on loan with MLS side Vancouver Whitecaps during the 2016 season, playing 24 times, before short spells with Falkirk, Dunfermline Athletic, Dundee United and Queen of the South.
He joined League Two side Cove Rangers in September 2019 on a deal until January 2020, playing ten games and scoring three goals.