A male suspect was shot dead by an armed police officer.
Another six people are in hospital for treatment to their injuries, including a police officer who suffered knife wounds.
Police said the incident was now contained and did not present a threat to the wider public.
Armed police have sealed off West George Street and paramedics in hazmat suits were seen treating a person on a blood-stained pavement.
Eyewitnesses told Sky News they saw people, bloodied, being taken on stretchers from the Park Inn hotel.
Louisa, who was in a building on West George Street, told Sky News: "I saw people being treated with blood on the ground.
"I saw people running out of the hotel with the police shouting 'put your hands up, put your hands up, come out'.
"There were police cars, ambulances all over the street and they cordoned it off. Police were shouting to people in other buildings near the Park Inn hotel to stay inside and not come into the street.
"I saw at least three people injured and they were taken away in ambulances.
"There were quite a number of people coming out with their hands up, running down the steps of the hotel.
"I saw people with blood on them, all over the ground."
Sky News' home affairs correspondent Mark White said: "There are reports, in addition to the suspect who was shot dead by police, of fatalities.
"I'm not able to put a precise number on that. It was mentioned three, but we don't know if that includes the alleged armed attacker as well.
"At this moment in time we can say there are reports of fatalities but there is no precise number on that."
He added: "They're not in a position where they're yet determining that this is being treated as a terrorist incident, but sources I've been speaking to certainly are suggesting that it may well be heading in that direction."
"However, I would like to reassure the public that this is a contained incident and that the wider public is not at risk. Armed police officers attended the incident and I can confirm that a male suspect was shot by an armed officer.
"I would like to reassure the public that at this time we are not looking for anyone else in relation to this incident.
"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."
Home Secretary Priti Patel said she was "deeply alarmed" by the incident, while Scotland's first minister Nicola Sturgeon described it as "truly dreadful" and urged people to stay away from the area.
https://news.sky.com/story/armed-police-deployed-after-several-injured-in-serious-incident-in-glasgow-12015385