The alert came after terrified families were trapped in a tower block when a blaze broke out in the close.
It was the latest in a spate of fires at high-rises or tenements – all started in shared stairways – across the city.
No-one has been seriously injured, but Strathclyde Fire and Rescue's Assistant Chief Officer Lewis Ramsay says lives are at risk if these vandals strike again.
He said: "Until now we have been very fortunate, but I believe a person – or people – will be killed because of this reckless behaviour.
"The people that carry out these acts are putting others in extreme danger.
"It is so difficult to understand the mindset of these people and why they would want to do something like this. I have no doubt we will see a loss of life if this is to continue."
The latest incident was in a three-storey building in Banner Drive, Knightswood, when flames quickly spread through the ground floor.
Residents had to be rescued at about 9.15pm on Monday.
The firefighters needed breathing apparatus to get into the stairwell to tackle the flames and then had to use a high-pressure fan to clear the thick smoke.
A man – believed to be in his 70s – was taken to the Western Infirmary, where he was treated after breathing in smoke.
A full investigation into the cause of the blaze is being carried out.
That incident came just a day after firebugs set alight a wheelie bin and two foam-filled sofas at the bottom of the common stairway in Charlotte Street, in the East End.
As previously reported by the Evening Times, police are treating that fire as wilful.
Investigations are also continuing into two incidents in Toryglen where bins were also set alight.
In another two recent incidents, on the South Side, an elderly couple had to flee their home in Cathcart and a couple had to be treated for smoke inhalation in Pollokshields.
Mr Ramsay continued: "Very few of these incidents are accidental. Mostly they are instances of wilful fire raising and it is extremely risky.
"People have lost their homes because of this and we have seen a significant loss of property.
"There is also a huge cost associated with these crimes."
Mr Ramsay assured residents of tenements they are not in any specific danger – but he urged people to be more careful.
He said: "People should avoid lots of storage, in particular rubbish, and make sure property is secure.
"Our partners, including Glasgow City Council, are very good at uplifting rubbish and old furniture, so it is not difficult to keep the close clear.
"These incidents are not happening every day, but they are happening enough for something terrible to happen.
"I would urge people with concerns about this issue to contact the fire brigade. Nobody should have to tolerate wilful fire raising."
Strathclyde Fire and Rescue can be contacted on 01698 300 999.
Anyone with any information on any of the incidents should call police on 0141 532 2000 or Crimestoppers anonymously on 0800 555 111.