The MP for Beckenham, south-east London, was fined Â£600 after telling an activist to "go back to Bahrain".
The judge heard he got into a row with Sayed Ahmed Alwadaei in Westminster last December.
Labour and the Liberal Democrats had called for Stewart to lose the whip.
The 74-year-old is understood to have told the Chief Whip Simon Hart he wishes to surrender the whip until any future appeal is resolved.
BBC News has approached Stewart for comment.
Westminster Magistrates' Court heard on Friday that he had been attending an event hosted by the Bahraini Embassy when Mr Alwadaei shouted: "Bob Stewart, for how much did you sell yourself to the Bahraini regime?"
The MP, who was stationed in Bahrain as an Army officer in the 1960s, told the campaigner to "get stuffed" and added: "Bahrain's a great place. End of."
Mr Alwadaei - the director of advocacy at the Bahrain Institute for Rights and Democracy - challenged Stewart on his connections with the country, asking whether he had accepted any money from the Bahraini government.
Stewart replied: "Go away, I hate you. You make a lot of fuss. Go back to Bahrain."
The incident took place outside the Foreign Office's Lancaster House in Westminster.
In a post on X,after Stewart was found guilty, Mr Alwadaei said: "No-one should think twice about holding an MP or members of the government to account because of their skin colour.
"When I reported Mr Stewart to the Conservative Party, they didn't take action against him and when he was charged, they refused to suspend him.
"Given today's verdict, I expect them to take immediate action."
Chief Magistrate Paul Goldspring spoke of Stewart's "immense positive character" at the conclusion of Friday's trial, adding: "I accept he is not racist per se, but that is not the case against him.
"Good men can do bad things."
The MP was ordered to pay legal costs of Â£835, on top of his fine.
Bob Stewart has surrendered the Conservative whip while he considers appealing against his conviction for a racially aggravated public order offence, the BBC understands.