According to the community security organisation Shomrim, the suspect was seen “deliberately” setting fire to the pram and ran off when he was confronted.
A resident grabbed a bucket of water and put the blaze out, and no injuries were reported.
Most of the people in the block are Jewish and many are young families with babies and toddlers.
The Metropolitan Police confirmed that an investigation is under way and said officers are keeping an "open mind" about the man’s motive.
Shomrim attended the scene and said it recovered evidence believed to belong to the suspect.
The organisation is assisting police with their enquiries and supporting residents affected by the incident.
Monty Sternlicht, 18, who lives in one of the flats, said: "At about 4am yesterday, my mum, my brother Benny and I were woken by the fire alarm.
"We rushed out into the corridor. There was smoke everywhere. It was hard to breathe.
"It was very thick. It was chaos.
"Our next door neighbour said he had come out of his flat and seen the man next to the burning pram on the landing.
“He ran to fetch a bucket of water to throw on it and chased the man away."
The alleged arson attack on a pram in a stairwell in Golders Green (Credit: Shomrim/X)[Missing Credit]
Another resident said a neighbour claimed the suspect wrapped his own trousers around the pram before setting it alight.
Police are hunting for CCTV and doorbell footage.
The incident follows a spate of arson attacks on the Golders Green Jewish community, which began in late March with the burning of four Hatzola ambulances.
Members of the local Jewish community described their shock following the fire at the flats.
One resident told the JC: "We're all very worried at the moment. We're on edge. It's a terrifying time to be living around here."
He added: "We live in constant fear. It's horrific. There are young families with babies, toddlers and young children. When will this end?"
Another resident said police forensics officers remained at the scene throughout Tuesday, interviewing witnesses and seeking any doorbell camera footage.
A witness to the incident said the suspect appeared to be acting suspiciously before being challenged by residents.
"He was disturbed when he was seen acting weirdly," the resident said. "He was shouted at and then ran off when he was chased."
Shomrim said in a statement: “Residents reported witnessing a suspect deliberately start a fire in a communal stairwell before fleeing when challenged.”
A Metropolitan Police spokesperson said: "Police were called at 04:52hrs on Tuesday, June 2, after an empty pram was set alight by a man inside a block of flats on Bridge Lane, Golders Green.
"The fire was quickly put out by members of the public. No injuries have been reported.
"No arrests have been made and officers are keeping an open mind as to the man's motive.
"Enquiries continue and anyone with information that could help police is urged to contact 101 quoting CAD 7231/02JUN."
