Ketsbaia, 41, who signed a three-year contract on May 25, leaves the Pireaus club after a 2-0 away victory over Larissa and a goalless home draw with Kavala.
Olympiakos host Dutch side AZ Alkmaar at the Georgios Karaiskakis stadium on Wednesday in their first Group H match.
"Olympiakos announces the mutual solution of its collaboration with coach Temuri Ketsbaia," the club announced in a statement on its official website on Tuesday.
"The technical leadership of the team will be temporarily undertaken by Bozidar Bandovic. His assistant will be Andreas Niniadis."
Club spokesman Giannis Moralis urged the Pireaus club's fans to show their support on Wednesday.
"Our fans need to get behind the team," he told the Greek sports radio station Sentra FM.
"The club has passed through a tough 10 days. We want the supporters behind us because we are competing in the Champions League.
"Usually a change in coach gives a different impulse and climate in a team and this did not go well. As long as he was in charge there are a 1,000 reasons for this move.
"The team did not show the strength that we wished, neither were the results satisfactory. This was the only solution. There are no hidden reasons."
