Defender Mbulu, who was an unused substitute, was allegedly targeted while warming up on the touchline.
Police Scotland said two people had been arrested after game, which Hearts won 1-0 thanks to a 14th-minute goal by Peter Haring.
Hearts, who have said they are “cooperating fully” with police, announced on Sunday they were taking action.
Owner Ann Budge said: “”This behaviour will not be tolerated.
“The individuals involved have already been identified and have received immediate and indefinite bans.
“I’m so very disappointed that instead of being able to enjoy a good victory and staying at the top end of the table I’m having to comment on the entirely unacceptable behaviour of a minority of supporters.”
Police Scotland said: “We can confirm that two subjects were arrested at the Hearts v Motherwell match.”
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