Scotland Yard said they had opened the case following a complaint from Sayed Ahmed Alwadaei, who had a confrontation with the MP in central London.
The Beckenham MP also told the campaigner to "get stuffed".
Mr Stewart said he regretted the comments but insisted he was "not being racist in any way".
Mr Alwadaei, the director of advocacy at the Bahrain Institute for Rights and Democracy, challenged Mr Stewart on his connections with Bahrain outside an event to mark the National Day of Bahrain last Wednesday.
Footage of the incident outside the Foreign Office's Lancaster House shows Mr Stewart responding: "Bahrain's a great place. End of."
He later added: "Go away, I hate you. You make a lot of fuss. Go back to Bahrain."
After being repeatedly asked if he had accepted any money from the Bahraini government, Mr Stewart said: "You're taking money off my country, go away!"
Mr Stewart, a former Army officer who was stationed in Bahrain in the 1960s, later expressed contrition for his original remarks.
"The protesters persistently taunted me by saying I had taken money from Bahrain," he said.
"That deeply offended me. I certainly have not and told them so repeatedly.
"I admit I fell for the taunts and should not have responded which I regret. My comments were meant to tell them they could protest safely in Bahrain... Bahrain gets a very unfair press and I feel that strongly.
"I am sorry if anyone thought I was being racist in any way. Honestly I was not. I wish now I had not been drawn by the taunts (a mistake) but I was and I repeat, I apologise for that. The last thing I meant to be was racist as I have so many good Bahraini friends."
Mr Alwadaei fled Bahrain in 2011 after being arrested for taking part in anti-government protests and was able to claim political asylum in the UK in 2012.
Speaking following the incident with Mr Stewart. Mr Alwadaei said: "I still have the scars from where the authorities kicked me in the head, and if I went back to Bahrain I would face further torture and imprisonment. My family members are still suffering from reprisals."
He added: "I don't believe I would have been told to 'go back' to the country that violently tortured me if it weren't for the colour of my skin. No-one should be subjected to racial abuse."
Mr Alwadaei said he had also complained to the parliamentary commissioner for standards, Kathryn Stone and the Conservative party chairman Nadhim Zahawi.
A Conservative Party spokesman said: "We have an established code of conduct and formal processes where complaints can be made in confidence. This process is rightly confidential."
Watch: Video provided by activist Sayed Alwadaei shows his confrontation with Tory MP Bob Stewart