The London club had lodged an official complaint after Benayoun was barracked during a game in Kuala Lumpur on July 21, the first leg of Chelsea's Asian tour.
Chelsea initially played down the incident but went ahead with its complaint after reviewing the game. The club, which has since played games in Bangkok and Hong Kong without incident, said it is now happy to move on.
"We appreciate the prompt attention the Malaysian FA has given our complaint," it said in a statement.
"Chelsea Football Club is committed to eradicating all discriminatory behaviour from the game, and urges the MFA to take appropriate steps to stamp out this type of behaviour in future.
"The club and Yossi accept the apology, and the matter is now closed."
The Malaysian FA on Friday released a qualified apology to Chelsea and the player for conduct it said came from a small disruptive section of fans.
"The FA of Malaysia would like to strongly register that we do not condone any form of racism in football," it said.
"If such an incident did happen, we would like to apologise to the player concerned, and also to Chelsea FC."
The midfielder was booed and jeered whenever he touched the ball in during the 1-0 win against a Malaysia XI in the capital.
Benayoun was the first Israeli to play in Malaysia, which strongly supports the Palestinians and does not recognise Israel, maintaining no diplomatic ties with the country. Some 60 percent of Malaysia's population is Muslim.
Source: AFP
Source: AFP