"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.
It is the second failed comeback of the gruff 66-year-old after he flopped with the national team in his 2006-2008 spell having steered Argentina to successive Copa America victories in 1991 and 1993.
"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.
RIQUELME INJURY
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.
Bianchi, 60, would be a popular choice having led Boca to a string of titles including the Libertadores Cups three times in the early 2000s.
The beleaguered Basile, chatty and optimistic when he was unveiled at a July news conference, has spoken to media just once in the last three months, suffered rifts in the dressing room and was unpopular with several members of the club board.
Media reported that he had lost the support of Bianchi, who questioned his tactics for the match against River Plate.
River will be Boca's rivals again on Sunday in another mid-season friendly in Mendoza.
The Clausura championship, closing half of the two-tournament season, kicks off on the final weekend of January.
