Both teams had to play the final 20 minutes a man short at Tannadice after a tackle between Dundee skipper Stephen O'Donnell and United forward Johnny Russell sparked a melee between both sets of players.
When order had been restored the two players were given their marching orders by referee Calum Murray.
The SPL clash ended in a 3-0 win to United, with Russell on the scoresheet twice before his sending-off.
A statement from United read: "Dundee United have confirmed they have submitted an appeal to the Scottish FA relating to the red card dismissal of striker Johnny Russell during Sunday's SPL game v Dundee FC."
A Dundee statement on their own website read: "CEO Scot Gardiner have confirmed that the club is to appeal the sending off of captain Stephen O'Donnell at Tannadice."