"I don't want to go into the details, Anders will have to talk about that. But the threats have been serious enough," said Bo Karlsson, chairman of Sweden's football referees' association.
"We have spoken and I can confirm that he is quitting."
Swede Frisk, who was unavailable for comment on Friday, was in charge for Barcelona's controversial 2-1 first-leg victory over Chelsea in the Champions League first knockout round in Spain last month.
Chelsea manager Jose Mourinho said his Barcelona counterpart Frank Rijkaard talked with Frisk in the referee's changing room at halftime.
The London club were also unhappy when Frisk sent off striker Didier Drogba in the second half.
"None of the decisions Anders made during that match were wrong," Karlsson said.
Chelsea won the second leg 4-2 last Tuesday to claim a place in the quarter-finals following a 5-4 aggregate victory.
Frisk was also involved in an ugly incident in September when he was struck on the head by an object thrown from the crowd at AS Roma's Olympic Stadium during a Champions League match against Dynamo Kiev.
The Swedish referee abandoned the game, saying Roma could not guarantee the safety of the officials.
Frisk had been scheduled to referee the World Cup qualifying match between Estonia and Slovakia in Tallinn on March 26.
