The 46-year-old imam died of smoke inhalation trying to put out the fire.
The suspect entered the mosque armed with an axe and a knife, and spread flammable liquid before setting it alight, officials said.
He was grabbed and locked in a room by worshippers. Police said his motives were unclear but he had described himself as a Muslim born in 1978.
Around 100 people had gathered behind a police cordon around the Rida mosque - the largest Shia mosque in Brussels. Some were chanting Shia slogans, others crying, hugging or praying, the AFP news agency reports.
The imam was later named as Abdallah Dadou, a father of four children.
Belgium's interior minister Joelle Milquet said she was "very shocked by the events that have occurred".
Overnight, the mayor of Anderlecht, Gaetan Val Goidsenhoven, appealed for calm, saying it was "not only necessary to live side-by-side, but also to allow justice and the police to do their work".
Salafists Jean-Marc Meilleur, of Brussels' prosecutor's office, said police responded to reports of a fire at the mosque between 18:00 and 19:00 local time (17:00 and 18:00 GMT) on Monday.
"When they arrived at the location they realised that there was indeed a fire but also that a person had been detained by the mosque occupants," he said.
"It seemed that this person showed up and pulled out a knife and an axe, and that he spread flammable products, petrol we assume, in order to start a fire and threaten the people attending the mosque."
One other person was lightly injured, Mr Meilleur said.
It is not yet clear why the man attacked the mosque, but some local people said he was a "Salafist".
Salafists are very conservative Muslims who try to emulate the earliest followers of the Prophet Muhammad. Some Salafists preach hatred of Shia Muslims.
Isabelle Praile, a leading figure in Belgium's Muslim community, told national broadcaster RTBF that the mosque had been given a police guard some years ago because of threats from Salafists.