Dundee United fans ran on to the park when their side netted a last-gasp winner in a 3-2 victory over Ross County at the Global Energy Stadium in Dingwall.
Billy McKay scored a close range header for the Tannadice side - who came from behind to book a place in the semi-finals of the competition despite having been reduced to ten-men earlier in the game.
The goal sparked wild scenes amongst the visiting supporters - with many seen running on to the pitch to celebrate with the United team.
Police have confirmed that seven have so far been arrested - and that further enquiries will take place that could lead to further arrests.
Match Commander Colin Gough said: “It is disappointing that a small minority of fans were involved within disorder in the ground.
“Disruptive behaviour will not be tolerated in any format. Enquiries are continuing and there is potential for further arrests.”
A Police Scotland spokesman added: “Police Scotland can confirm that seven men have been arrested in connection with football related disorder at the Global Energy Stadium in Dingwall at the Ross County v Dundee United game.
“A report will be submitted to the Procurator Fiscal in due course.”
Before the match Dundee United had appealed for fans to stay in the stands regardless of events on the pitch.
In a statement on their website ahead of the clash, the club said: “All fans are respectfully reminded to conduct themselves in a manner that does not bring the club and its support into disrepute and to adhere to the ground regulations and code of conduct of the Global Energy Stadium.
“All fans are advised to remain within the stand and to refrain from entering trackside or the field of play.”