The fire, contained to the sixth floor of the 20-storey Napier Street building, caused the evacuation of 300 residents about 5am on Wednesday.

A man with serious burns to the face, arms and back was taken to The Alfred hospital where he remained in a critical condition on Wednesday evening.

The cause is under investigation, but police say a mattress outside a unit was set alight.

The Department of Housing has denied there were problems with the alarms, saying the Metropolitan Fire Brigade had advised both the alarms and sprinklers worked as expected.

Housing Minister Martin Foley said he was confident that the agreed procedures between the MFB and Office of Housing had worked properly, including fire alarms.

"I'm advised the smoke detectors worked," he said. "I'm advised they are checked monthly."

A spokeswoman for the minister later said a report showed the alarms were working on March 1.

Mr Foley said the evacuation proceeded according to protocols but some people were "missed" at the top of the building.

But two residents of the sixth floor - where the department said there had been damage to the electrical wiring - said alarms did not go off on their floor.

Hassan Yagob, who lives with his wife and four children, including a newborn, said he was alerted to the fire after hearing yelling, but not alarm went off.

"No alarm, nothing," Mr Yagob said.

He grabbed his wife and children and escaped with them down the stairs along with an elderly neighbour as thick smoke filled their floor.

"I'm lucky I'm still alive," he said.

Lin, who did not want to use her surname, said the alarm went off inside her apartment when she opened her door and let smoke in, but it was not operating in the corridor.

"There should be an alarm on our floor and in our home," she said.

Sisters Sabuha and Paula Dzaferovski live on the 14th floor and say they could hear an alarm coming from the ground floor, but none went off inside their apartment.

They said they thought it was a false alarm at first until they smelt smoke.

"We literally had to wet towels and put them over our mouths," Paula Dzaferovski said.

"If all the alarms went off - the individual alarms - everyone would've opened their doors and gone 'OK, there's smoke, we've got to get out' instead of wait until the last minute.

"There could've been a situation where there's no way you would've made it down the stairs, there was too much smoke. You would've been stuck up there."

Hoda Omar, who lives on the seventh floor with her three young children, said the alarms did not go off on her floor either and she was alerted to the fire by the smell of gas and smoke.

Another resident, Brandon Sahnkovich, said fire drills had taken place in the past, but were ignored by some residents.

A department spokesman said mandatory inspections of the firefighting systems are undertaken monthly and the last inspection was on March 1.

"All apartments are fitted with sprinklers and fire alarms, which the Melbourne Fire Brigade has advised worked as expected during this fire," he said.

Mr Foley said one firefighter removed his breathing apparatus and gave it to a pregnant woman on level 10.

The firefighter was then hospitalised for smoke inhalation.

"I think this reflects the best traditions of what our first responders and fire fighters are well regarded for in our community," Mr Foley said.

Two men with smoke inhalation were taken to Royal Melbourne and St Vincent's Hospital in a stable condition, while two women with existing medical conditions were taken to St Vincent's Hospital in a stable condition.

with Neelima Choahan