Officers were called to a suspected shooting at an apartment in Hovsjö around 23:11 local time (22:11 GMT) on Wednesday.
The man, who has not been named by police, was found with gunshot wounds and taken to hospital. The force announced he had died on Thursday morning.
Local media reported that Mr Momika had been livestreaming on social media around the time he was shot.
Mr Momika, an Iraqi living in Sweden, was charged in August alongside one other with “agitation against an ethnic group” on four occasions in the summer of 2023.
The verdict, due to be delivered on Thursday, was postponed after it was “confirmed that one of the defendants had died”, Stockholm District Court said.
Prime Minister Ulf Kristersson said Sweden’s security services were involved in the investigation because there was “obviously a risk that there were links to foreign powers,” SVT reported, external.
Mr Momika carried out a series of anti-Islam protests, sparking outrage in many Muslim-majority countries.
Unrest took place at the Swedish embassy in Baghdad twice, while the Swedish ambassador was expelled from the city amid a diplomatic row.
Swedish police had given Mr Momika permission for the protest in which he burnt the holy book, in accordance with the country’s free-speech laws.
The government later pledged to explore legal means of abolishing protests that involve burning texts in certain circumstances.
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