"We have taken the decision by mutual accord not to extend the work the Argentine coach was carrying out," they said in a statement.
La Volpe, a former goalkeeper who was in Argentina's 1978-World cup winning squad, was in his second spell with Atlas having also coached them from 1997 to 2001.
"The truth is that Ricardo knew (of the decision) eight days ago," Carlos Martin del Campo, president of the Guadalajara-based club, told Mexican radio.
Atlas, who have not won a league title since the 1950s, failed to reach the knockout rounds of the Apertura championship after picking up only five wins and 18 points from 17 matches in the qualifying phase. He won 10 of his 34 matches since taking charge in January.
The moustachioed 57-year-old La Volpe, often abrasive in manner but widely popular for his tactics, was in charge of Mexico from 2002 until the 2006 World Cup in Germany where they lost in the second round to Argentina in Leipzig.
Having spent most of his coaching career in Mexico where he has also been in charge of America, Atlante, Guadalajara, Puebla, Queretaro y Monterrey, La Volpe returned to Argentina after the 2006 World Cup.
He lasted less than six months at Boca Juniors, resigning after they lost the Apertura title-playoff to Estudiantes. A year later he also resigned after an unsuccessful stint with Velez Sarsfield and returned to Mexico to take charge of Monterrey.
The first legs of the Apertura quarter-finals will be played this weekend.
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