The fans were demanding an end to unclear ownership and financial dealings at the oldest Czech club, who have suffered heavy debts and are on the brink of losing their first division licence for next season.
Some 1,500 fans went onto the pitch before the start of the cup semi-final against Olomouc, demanding an explanation from management on how it would overcome the debts.
They allowed the game to go ahead after pleas from the players, but they stormed the pitch again after half-time, forcing officials to call off the game with the score at 1-1.
"We want the truth. Long live Slavia," the fans chanted.
New agency CTK reported some of the fans clashed with riot police, damaged equipment at Slavia's new Prague stadium and tried to attack club director Miroslav Platil.
The club could face a 3-0 walkover loss for the incident.
"We understand the fans to a certain extent, but the players are disappointed," Slavia spokesman Ondrej Zlamal said in a statement.
"They fought for a place in Europe (a spot in the Europa League), they have not seen pay for four months but still made it into the semi-finals. They believed they could win the cup but now they did not get the chance to get a better result than 0-3."
Slavia, who last won the league title in 2008 and 2009, have had a bleak season in the league and are in 10th place, with the cup being the only chance to book a spot in Europe next term.
Slavia said a potential investor had paid 30 percent of wages owed to players on Thursday to ease the situation at the club, established in 1892 and the most famous Czech side alongside cross-town rivals Sparta Prague.
Slavia, known for their traditional red and white jerseys and red star symbol, have won the Czech title 17 times.
The Czech Football Association has ruled not to give Slavia a first division licence for next season due to their debts. The club can still win back the licence if they find funding by the end of May.
Slavia have had an unclear financial and ownership structure for years, and the Czech press has been rife with speculation over which entrepreneurs were the ultimate owners.
