The club made the announcement in a statement on their website (www.udlaspalmas.es) after the 3-2 defeat at home to Deportivo La Coruna in the King's Cup, even though they still reached the last 16 of the tournament 6-4 on aggregate.
A former assistant to Rafa Benitez at Liverpool and Valencia, Ayestaran holds the record for the most consecutive defeats in Spanish top flight history, losing 13 games in a row in charge of Valencia last season and Las Palmas this term.
He brought that dismal run to an end with a 1-1 draw at Real Sociedad last Sunday, which took the side off the bottom of La Liga and up to 19th in the standings.
Ayestaran took charge of Las Palmas on Sept. 27 after Manolo Marquez resigned from the role following two wins and four defeats. His only victory with the Canary Island side was a 4-1 win over Deportivo in the first leg of their last 32 Cup tie.
The club said assistant coaches Paquito Ortiz and Rafa Cristobal would take charge of the team until a replacement was announced.
Former Rayo Vallecano coach Paco Jemez, who had a brief spell in charge of Las Palmas between 2010-11, ruled himself out of the vacant role for the immediate future but said he could be tempted to take over in early 2018.
"I'm grateful to (club president) Miguel Angel Ramirez for his efforts to make me coach but now is not the time, I can't leave my family alone again," Jemez, who left his role at Mexican side Cruz Azul, told the club's official radio station.
"But sooner or later I will end up at Las Palmas."
(Reporting by Richard Martin Editing by Jeremy Gaunt)
