Racing, one of Argentina's so-called Big Five clubs, are bottom of the 'Inicial' championship with two points from seven matches.
"The board of directors, at their weekly meeting on Wednesday night, decided one of those mainly responsible for managing professional football should leave his post," the club said on their website (www.racingclub.com.ar), referring to Ayala.
First to go three weeks ago was coach Luis Zubeldia after his promotion of a group of talented young players backfired this season with a draw followed by three defeats.
Ayala, criticised for poor recruiting during the off-season, appointed experienced former Boca Juniors coach Carlos Ischia in his place but he is struggling to turn the tide.
The board are divided into two factions, one headed by president Gaston Cogorno, and another by vice-president Rodolfo Molina who led the calls for Ayala's dismissal.
The mood at Racing now is a far cry from the one in June when they celebrated three victories in the run-in to the 'Final' championship and the relegation of bitter rivals Independiente.
Ayala, 40, returned from 14 years in Europe with Napoli, AC Milan, Valencia and Real Zaragoza to end his playing career at Racing in 2011.
He won 115 caps as a central defender and helped Argentina win the Olympic gold medal at the 2004 Athens Games.
(Reporting by Rex Gowar; editing by Tony Jimenez)