"A man who has done a lot for the club has just resigned and (reserve team coach) Abel Alves is taking interim charge," Boca president Jorge Amor Ameal told a news conference.
Basile, whose side fell to River in Mar del Plata on Wednesday, was unable to build a successful team in his second spell at Boca since his return last July having lifted several titles with the club between 2005 and 2006.
"We're going to take the necessary time to make a decision (on a new appointment), Alves is a man of the club," said Amor Ameal referring to the 51-year-old former Boca midfielder, who has been caretaker twice before.
Amor Ameal denied categorically that general manager Carlos Bianchi would be first choice to succeed Basile, saying "Bianchi does not want to coach."
Boca, like River, had a troubled 2009. It will be the first time in 15 years that neither of the country's "big two" will take part in the Libertadores Cup, South America's top club championship.
Boca had hoped Basile's return in July would spark a recovery but he had a tendency to rely too heavily on the veterans, playmaker Juan Roman Riquelme, striker Martin Palermo and goalkeeper Roberto Abbondanzieri.
Riquelme, a Basile favourite with Boca and Argentina, missed more than half last year's Apertura championship through injury and the team felt his absence badly.
Wednesday's non-competitive match in the seaside resort of Mar del Plata, played as fiercely as the league derbies between the arch-rivals, was Riquelme's return from injury.
River will be Boca's rivals again on Sunday in another mid-season friendly in Mendoza.
