A firefighter could be seen perched on a ladder spraying water onto the burning building as it fell.
Jalal Maleki, a fire department spokesman, told Iranian state television that 10 fire stations responded to the blaze, which was first reported around 8 a.m. local time (11:30 p.m. ET on Wednesday).
A large number of businesses in the building are believed to be involved in the textile and garment industries.
The owner of a nearby grocery store, who was forced by police to leave the area, told Reuters by telephone that "it was like a horror movie. The building collapsed in front of me."
The semi-official Fars news agency said police had cordoned off the British and Turkish Embassies which are situated nearby.
The tower was built in the early 1960s by Iranian Jewish businessman Habib Elghanian and named after his plastics manufacturing company. It was the tallest building in the city at the time of its construction.
Elghanian was tried on charges that included espionage and executed in the months after the 1979 Islamic Revolution that brought the current ruling system to power — a move that prompted many members of the country's longstanding Jewish community to flee.
Eoghan Macgurie is a freelance journalist contributing to NBC News from London.
Ali Arouzi, The Associated Press and Reuters contributed.