Police Scotland reported a 43 per cent rise in domestic violence on 17 April, the day of the game at Hampden Park.
There were a total of 210 reported incidents throughout Scotland, compared to 146 on an average Sunday.
Most of the alleged crimes took place in and around the Glasgow area, police confirmed.
Chief Superintendent Barry McEwan, head of Police Scotland’s licensing and violence reduction division, said: “Following the recent Scottish Cup semi-final between Rangers and Celtic at Hampden it is disappointing to see an increase in reported incidents of domestic abuse.
“Dealing with this remains a priority for Police Scotland, one which we pro-actively addressed prior to this match taking place.
“Our officers have detected around 60 per cent of the domestic crimes committed that day and will continue to pursue the outstanding crimes and target those offenders that cause harm to their victims.”
He added: “Our priority is always to protect victims from potential harm and we have been directly engaging with known offenders to remind them of the consequences of their actions should they offend.”
Ch Supt McEwan said excess drinking was behind most incidents.
He added: “Although we can’t attribute all of these incidents of domestic abuse directly to the Rangers and Celtic match, these figures underline that this event often leads to individuals having too much alcohol to drink which unfortunately lead to anti-social behaviour, violence and domestic abuse.
“There was a clear proactive strategy ahead of last week’s fixtures, which included working with partners to address violence and disorder, domestic abuse and licensing issues.”
Meanwhile, a futher 18 arrests were made in and around Hampden and in Glasgow on the day of the semi-final, which Rangers won 5-4 on penalties.
They were charged with offences including sectarian, threatening or abusive behaviour, assault and running on to the pitch.