People were evacuated on West George Street following the incident at the Park Inn Hotel.
A suspect has been shot dead by police after six people including an officer were injured in the attack.
All six injured people, including the officer, are being treated in hospital.
There is a heavy police presence at the scene and the public has been urged to avoid the area which has been sealed off.
In a statement on Twitter, assistant chief constable Steve Johnson said: “The individual who was shot by armed police has died.
“Six other people are in hospital for treatment to their injuries including a police officer, who is in a critical but stable condition.
“We are continuing to deal with the incident on West George Street #Glasgow and would ask people to avoid the area.
“We would urge the public not to speculate about this incident or share unconfirmed information on social media.”
In an earlier tweet, he said the incident had been contained and the wider public were not at risk.
He said: “I would like to reassure the public that at this time we are not looking for anyone else in relation to this incident.”
David Hamilton, Scottish Police Federation chairman, said: “Whilst there is understandable and considerable public interest in the major incident in Glasgow earlier today, our focus at this time is in assisting the family of our colleague who has been seriously injured.
“This is obviously an anxious time for them and we ask that they be left alone as their attentions are very obviously directed towards the care of their loved one.
“Our thoughts, prayers, and best wishes are with our colleague, his family and friends, and all colleagues affected by this incident at this time.”
Scotland First Minister Nicola Sturgeon tweeted: “Please follow advice to avoid the West George Street area of Glasgow while Police Scotland deal with this ongoing incident.”
Prime Minister Boris Johnson tweeted: “Deeply saddened by the terrible incident in Glasgow, my thoughts are with all the victims and their families. Thank you to our brave emergency services who are responding.”
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