A BBC reporter in the city says the burial had to be halted at one stage as police struggled to control the crowd.
Mr Kanumba was famous for roles in Tanzania's soap operas and films shown all over east and central Africa.
Police say Mr Kanumba, 28, died after an accidental fall during an argument with his girlfriend Elizabeth Michael.
Ms Michael - also an actor, known as "Lulu" - is being held for questioning, Kinondoni Regional Police Commander Mr Charles Kenyela told the BBC.
The BBC's Erick Nampesya in Dar es Salaam says many people flocked to the funeral service to see for themselves that Mr Kanumba was dead.
President Jakaya Kikwete said he delayed a foreign trip when he heard the news of Mr Kanumba's death.
He praised the "talented young man who was playing a big role to develop the movie industry and marketing Tanzania abroad".
Nicknamed "The Great", Mr Kanumba was a household name in Tanzania.
He starred in most major "Bongo" films, as local movie industry is called.
He had also recently become popular in Ghana and starred in Nigeria's Nollywood films.
More than 30,000 people in Dar es Salaam have attended the funeral of Tanzania's most popular film star Steven Kanumba, who died on Saturday.