Kick It Out's demands come after Chelsea midfielder Yossi Benayoun was targeted for abuse during a game in Kuala Lumpur.
The Barclays Premier League club had initially dismissed the jeering directed at the Israeli player every time he touched the ball as the consequence of a bad tackle early in last Thursday's game against a Malaysian XI.
But Chelsea released a statement overnight to say they have complained to the Malaysian football association, who have yet to formally respond.
A spokesman for Kick it Out told Press Association Sport: "Kick It Out supports the action taken by Chelsea on this matter.
"After working with the club on the recent 'Y-Word' film, aimed squarely at challenging anti-semitism and anti-Jewish abuse and featuring Frank Lampard, it's a strand of discrimination which is front of mind for both organisations.
"In addition, the campaign is keen to engage with Malaysian authorities around the issue and how football can play its part in educating mass audiences to become better versed on issues around faith and religion."
In April this year, Chelsea's England midfielder Lampard lent his support to the anti-semitism campaign backed by Kick It Out, in a film written and produced by comedian David Baddiel.
Agency reports from the region immediately after last Thursday's match at the Bukit Jalil National Stadium, watched by 84,980 spectators, had said the abuse directed at Benayoun was anti-semitic.
When briefing the media after the match, Chelsea played down that suggestion - but, having reviewed the match, they have changed their mind with the club set to fly home at the weekend following the Barclays Asia Trophy.
A Chelsea statement read: "Notwithstanding most fans behaving appropriately on the night, we believe Yossi was subjected to anti-semitic abuse by a number of supporters at the game.
"Such behaviour is offensive, totally unacceptable and has no place in football.
"The club did not make representations at the time as it was initially unclear as to the nature of the abuse Yossi received, as several players from both teams experienced similar treatment, sometimes louder and longer.
"However, having taken time to consider the issue fully, it has become apparent that a formal complaint was necessary.
"Our stay in Malaysia was, on the whole, a very positive experience for all the team travelling on the pre-season tour. It is a shame, therefore, that the behaviour of a minority of supporters is also a memory we take away."
After Chelsea tackle Aston Villa in Hong Kong on July 30, Andreas Villas-Boas' squad will return to London as they fine-tune preparations for the new domestic campaign, which starts at Stoke.
Midfielder John Obi Mikel maintains the Blues must face the challenges of their big-spending rivals head on.
Quoted in the London Evening Standard, he said: "It will be tough to win a trophy this year, I think this will be the toughest season Chelsea will have. Everywhere teams are spending money or getting better, but Chelsea are tough, too.
"We know we need to improve but the most important thing is that we know we can improve. We should not be afraid."