Logan, who has been at the club since 2014, was part of the side that beat Steven Gerrard's Rangers in the Scottish League Cup semi-final at the weekend.
Lewis Ferguson was the only goalscorer at Hampden Park just 11 minutes before time, taking the Pittodrie side through to the final against Celtic.
A video on Snapchat has emerged of the defender speaking after the game, in which he launches in to a bad language-filled rant about the victory.
"He bought my dinner, we f***** his team yesterday, the most I can do is let him come round and watch the football at my house.", before signing off by saying 'F*** Rangers'.