The incident is not being treated as terrorism, Police Scotland has said.
All six injured people, including the 42-year-old officer who is in “critical but stable” condition, are being treated in hospital. He was later named as constable David Whyte.
The other victims are men aged 17, 18, 20, 38 and 53 and have not yet been named.
There is currently a heavy police presence around the Park Inn in West George Street with more than a dozen emergency vehicles. Authorities said the incident was “contained” and there is no danger to the general public.
HuffPost UK understands the Park Inn Hotel, which armed police were seen entering is temporarily home to asylum seekers – though it is not known if there were other guests as well. Two receptionists are believed to be among those injured.
Police Scotland 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.”
One witness, who gave his name as John, told the PA news agency he saw two people stabbed in the hotel. He said he came down from the third floor to see the reception area covered in blood.
“One receptionist had been stabbed behind the receptionist desk,” he said.
“And then when I went down to the entrance I shouted at him and told him to stay calm and I will call for help.
“When I went to the entrance I saw another receptionist [...] had been stabbed. There were two police officers there assisting him.”
Addressing the attack, first minister Nicola Sturgeon said: “First and foremost my thoughts are with all those people who have been caught up in this terrible incident, particularly the six injured people taken to hospital for treatment, as well as residents and staff at the hotel.
“While such a serious incident is rare in Scotland it is another reminder of the courage and professionalism of our police officers who are willing to run towards danger in order to protect the lives of others.”
Greater Glasgow Police tweeted: “Emergency services are currently dealing with an incident on West George Street in Glasgow.
“The street is currently closed off and the public are asked to avoid the area at present.
“The situation is contained at this time and there is no danger to the general public.”
Craig Milroy, who saw the aftermath of the incident from an office building nearby, said he had seen four people taken away in ambulances.
“After that we saw commotion, ambulances further up and we saw armed police all running into the hotel next to the Society Room,” he said.
“We were still standing outside. After that the police all came down. The riot police and triage team told us to go back in and lock the door.”
Witnesses posting on social media reported a large police presence including armed officers and riot vans.
A traffic information bulletin issued by Glasgow City Council said: “Due to a serious police incident the following roads are currently closed until further notice.”