Fermanagh's All-Star nominee Sean Quigley has also been given a one-match ban following an incident in the Athletic Grounds game.
Both counties can appeal against the fines while there may also be an attempt to overturn Quigley's ban.
Several players from both teams got involved in jostling in the tunnel.
A row involving up to 20 players erupted in the wake of Tony Kernan's black card for tripping Quigley.
Tempers flared as referee Cormac Reilly blew the half-time whistle and the row continued as the players made their way down the tunnel.
Reilly booked Aidan Forker and James McMahon before the second half started while the game also had numerous late and cynical hits.
As it stands, Quigley's ban will rule him out of Sunday's Division 2 game against Laois.
Both Castlebar Mitchels and Crossmaglen Rangers have also been fined by the GAA's Central Competitions Control Committee following disturbances on the sideline in the closing stages of their recent All-Ireland Club Football semi-final.
Castlebar have been hit with a 1,500 Euro penalty with Crossmaglen fined 1,000 Euro.
Once again, appeals are highly likely.
Armagh and Fermanagh have been handed 5,000 Euro fines following the half-time disturbances in last weekend's Football League Division 2 game.