Fans took to the field after Dungnan Clarkis won their first Tyrone Football title in 64 years.
Police said they are investigating a GAA match in Tyrone County on Sunday to see if Covid-19 regulations have been violated.
Dungannon Clarkes won his first Tyrone Football title in 64 years when he defeated defending champion Trillick 8-7 in a thrilling penalty shootout at Omagh.
Fans took to the field, leading to concerns about social distancing.
First Minister Arlene Foster said she was “extremely concerned” after seeing the pictures of the match.
PSNI Ch Supt Ryan Henderson said: “We are aware of an accident in the GAA match in Umag yesterday and will review all available evidence to identify any potential breach of NI 2020 health protection (coronavirus restrictions) or any other law specified with respect to any individual.”
Ulster GAA said in a statement that while it was a moment of “great joy”, the celebrations on the pitch violated GAA protocols and public health guidelines.
The statement added that “the dramatic nature of the conclusion of the match has probably increased the abundance, but we are living in a pandemic and the scenes after the match did not portray Al Ittihad in a positive way.”
Joyful spectators poured onto the field after the team won the Tyrone Senior Championship.
Ms Foster said that despite the fact that the victory was “a milestone for Donganon, Covid-19 does not respect victories.”
She said that “other events” were “responsible” and that “sports and health would be the losers.”
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GAA said protocols surrounding all aspects of gaming have been introduced and “for the most part, observed globally”.
“The Civil Aviation Authority has acted in a positive way since the outbreak of the epidemic, with attendance at the Games strictly regulated,” she said in a statement to the BBC.
“Our supporters have responded positively and responsibly, but last night’s scenes undoubtedly put GAA members and their community at greater risk of Covid-19.”
The association called on people to act responsibly.
“Last night’s scenes cannot be repeated or we will risk returning to a center where all matches will be played behind closed doors,” she said.
Sinn Féin MLA of South Down Sinéad Ennis said GAA has “led by example through this pandemic”.
“Our clubs and county councils have been the vanguard of the community response to Covid-19.
“We will not allow anyone to scapegoat our games,” she said on Twitter.
A spokesperson for the Department of Communities said that at the beginning of August, the CEO announced that some spectators could attend matches or sporting events organized in the open air.
“The administration has issued guidelines to assist sports administrative bodies, clubs and stadium operators to comply with the regulations, which have provided guidelines regarding the safe return of a limited number of spectators at outdoor sporting events,” he said.
“It included details of how bystanders would follow directions and highlighted the behavior required of bystanders attending events to help reduce the potential spread of Covid.”
In July, GAA said that up to 400 people, including match essentials, would be allowed to attend some GAA matches in Northern Ireland.
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