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.

Rod Mackenzie, described as a life-long crofter, was one of six commissioners elected in March and represents the East Highlands.
Mr Ewing said the appointment would bring stability to the Crofting Commission.
The regulatory body had been involved in a lengthy row that saw calls for the last convener to resign.
Earlier this year, Scottish ministers urged for action to address "worrying failures" indentified by a review of the commission.
The review ordered by the government found "personality clashes" amid issues with management at the organisation.
Crofting is carried out in the Highlands, Northern and Western Isles and Argyll.
Mr Ewing said: "As a life-long crofter, Mr Mackenzie will bring a wealth of knowledge and experience to the role and I look forward to working collaboratively with him in the future.
"With the appointment of the new convener, the creation of the new board of commissioners and the recruitment of a new chief executive earlier this year, I believe crofting can look forward to a period of stability and a positive focus on issues that will greatly improve the lives of those living in remote and rural areas."
Mr Mackenzie said he was delighted to be selected for the role.
He said: "We've had several meetings of the board of commissioners since the elections in March, both for business and for training as a new group coming together and I've been impressed by just that - how everyone wants to come together, to do a good job for crofting.
"And what I've quickly learnt is that it is no simple thing. As a public regulator, you are working within constraints - there's no magic wand.
"But what there is, is the will to work together to make a difference."
Armagh and Fermanagh have been handed 5,000 Euro fines following the half-time disturbances in last weekend's Football League Division 2 game.
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A new convener of the Crofting Commission has been appointed by Rural Economy Secretary Fergus Ewing.