Fire crews were called to the flat above a newsagents in Albert Road after the occupants discovered the blaze in the stairway at the rear of the building just before 6 p.m.
Barnoldswick Watch Manager Mick Strickland said it appeared a pile of newspapers and magazines had been set alight deliberately.
He said: “We are treating it as suspicious and have informed the police.
“A family with three children lives at the flat. The children were not home at the time of the fire but there were three adults inside.
“They thought something must be happening in the kitchen when they smelt the smoke and discovered the fire when they opened the front door.
“They made an attempt to put out the fire with their own extinguisher, and we completed the job on arrival.
“There was some damage to the entrance hall carpet and walls, and slight smoke damage to the first floor lounge and kitchen. We were at the scene for about an hour.”
Watch Manager Strickland said that the fire could have had much more serious consequences, as the stairway set alight was the only entrance or exit to the flat.
“We could have been faced with a really awful situation.
“Fortunately, nobody had any injuries and once they had been checked out by paramedics, declined hospital treatment.”
A spokesman for Pendle CID said an investigation had been launched into the cause of the fire as officers liaised with Lancashire Fire and Rescue Service.