Olympiakos must close the lower tier of the north stand at the Georgios Karaiskakis stadium for the last-16 first leg against Manchester United on February 25 and have also been fined 30,000 euros (£25,000).
UEFA imposed the penalties following incidents during Olympiakos' home Champions League Group C game against Anderlecht on December 10.
A UEFA statement read: "Olympiakos have been sanctioned for the racist conduct of supporters, insufficient organisation (of UEFA Safety and Security Regulations), the setting-off of fireworks and the use of a laser.
"There will be a partial closure of the Greek club's stadium - the lower tier of the north stand - for their next UEFA competition home match. They have also been fined 30,000 euros."
Zenit St Petersburg have also been similarly punished for incidents in their Champions League Group G game at Austria Vienna on December 11.
Zenit must close part of the Petrovski Stadium for the last-16 home match against Borussia Dortmund on February 25 and have been handed a 40,000-euro fine.
UEFA said: "Zenit have been penalised for the racist behaviour of fans - namely the displaying of a banner - the setting-off and throwing of fireworks and crowd disturbances.
"There will be a partial closure of the Russian team's stadium - specifically the area housing the club's ultras - for their next UEFA competition home game. Zenit have also been fined 40,000 euros."
Olympiakos have appealed against the decision.
Press spokesman Kostas Karapapas said: "The punishment is because of one particular banner which as soon as it was seen was taken down and that is why it is harsh to say the least.
"There was no racist slogan or racist banner, and no racist chanting or songs were heard during the match with Anderlecht.
"The punishment from UEFA is a first level decision and we have submitted an appeal to try to ensure that our stadium is full for the match against Manchester United."