Thousands of Hibs fans streamed on to the pitch at the final whistle at Hampden Park and fighting broke out when some Rangers fans then got past stewards.
Police horses were eventually brought on to restore order as police and stewards struggled to cope.
Hibs won the match 3-2 with a David Gray goal in injury time.
Rangers players appeared to be goaded by Hibs supporters as they tried to leave the pitch.
Hampden officials said the players would not return to the stand to collect their runners-up medals, receiving them in the changing room instead.
Police horses were last needed at the 1980 Scottish Cup final between Celtic and Rangers.
As Hibs fans returned to the stands part of the pitch was ripped up and the goal posts were broken by people climbing on them.
