Fighting broke out when dozens of Celtic supporters invaded the pitch to celebrate their quarter-final victory.
That sparked an incursion from hundreds of Rangers fans, who attempted to attack their Old Firm rivals.
Missiles and pyrotechnics were thrown before police and stewards finally formed a barrier across the pitch.
Fans continued to trade insults from either side of the barrier before order was restored.
The ugly scenes came in the first Old Firm derby for almost a decade to feature a large allocation of tickets for away fans.
Following numerous hooligan clashes in previous meetings between the Glasgow rivals, away supporters were banned from the matches in 2023, before being allowed to return on a reduced basis last year.
The Scottish Cup tie was seen as a test case for the return of bigger numbers of away fans, but that plan is unlikely to proceed after the clashes at Ibrox.
Celtic won 4-2 on penalties following a 0-0 draw after extra time.
Martin O'Neill's side moved into the semi-finals despite failing to register a single shot on target in 120 minutes.
In the shoot-out, Rangers captain James Tavernier hit the bar with the first penalty before Djeidi Gassama blazed over.
Tomas Cvancara converted to seal Celtic's victory before chaos reigned.
Despite amassing 24 shots and having a goal wiped out by VAR following a handball by Emmanuel Fernandez in extra-time, Rangers once again stumbled against their hated neighbours.
The defeat was a bitter blow after Rangers blew a two-goal half-time lead in their 2-2 draw with Celtic in the Scottish Premiership at Ibrox last weekend.
Rangers and Celtic both trail leaders Hearts in the Scottish title race.