An eyewitness told Sky News she had seen several people covered in blood being treated by emergency services after the incident at a city center hotel, and armed police on the scene, at around 1:15 p.m. (1215 GMT).
Police said six men, including the 42-year-old police officer in a critical but stable condition, had been hospitalized. Earlier reports had said three people, including the suspect shot by police, had died.
Authorities have yet to say what the motive for the attack was.There is currently no indication the attack was a terrorist event, a Western security source told Reuters.
Police Scotland Assistant Chief Constable Steve Johnson said the incident had been contained and there was no wider risk to the public.
"The individual who was shot by armed police has died," Police Scotland said in a statement, adding that they were not looking for anyone else in relation to the incident.
"We would urge the public not to speculate about this incident or share unconfirmed information on social media."
One eyewitness in the hotel described the scene as "full of blood".
"I was in my room and I heard loud screams from downstairs," a man who gave his name as John told the BBC.
"I got worried and went to check what was going on. When I opened the lift it was all blood."
Police Scotland said its injured officer was in a critical but stable condition.
Prime Minister Boris Johnson said he was "deeply saddened by the terrible incident in Glasgow."Last week, three people were killed in the southern English town of Reading when a man wielding a five-inch knife went on the rampage in a park. Police said they were treating that incident as terrorism.