Sukhbir Singh had reportedly made some controversial decisions while officiating last Saturday's International Champions Cup (ICC) match at the National Stadium in Singapore, where Inter Milan beat Chelsea by 2-1.
Mr Singh awarded a penalty to Inter after striker Stevan Jovetic was brought down by Chelsea full-back Cesar Azpilicueta, and the second was disallowing a late equaliser by Blues forward Michy Batshuayi.
Fifa match agent Baljit Rihal tagged Kick It Out who said that it had "received reports from the public on the racist abuse on social media aimed towards Singaporean Sikh referee during Chelsea's friendly against Inter Milan".
Some netizens took to Twitter to criticise Mr Singh's decisions and commented on his ethnicity.
"I wouldn't say I'm affected by it because I haven't read the tweets, but that doesn't mean I condone racism. It's (racism in football) something that definitely needs to be looked into. There should not be any bias towards anyone's race," Mr Singh was quoted as saying by The Strait Times.
Mr Singh has called for unity within the football community and said everyone should be allowed to believe in what they believe in freely and participate in what they want to participate in, especially when it comes to sports. Sports is supposed to unite people and not divide us, he said.
The anti-discrimination bureau 'Kick It Out' is investigating the incident, a move praised by Mr Singh.
He added that he had not experienced any racial abuse while refereeing locally, and has "not come under any circumstances where a report was needed".