"The incident is not being treated as terrorism and our investigation is continuing into the circumstances," Assistant Chief Constable Johnson said.
"There is no wider risk to the public, however, the street remains closed and people should avoid the area," he said.
Scottish First Minister Nicola Sturgeon said the reports were "truly dreadful" and she was being updated.
"It's been a dreadful afternoon for the city of Glasgow," she said. "Clearly there is already much speculation around this incident, which remains under investigation".
Police said they were on the scene within two minutes and the incident was quickly contained.
An eyewitness told Sky News she had seen several people covered in blood being treated by emergency services after an incident, and armed police at the hotel.
Images on social media showed armed police entering a building with emergency vehicles outside. One witness also claims to have seen seven people taken out of a building by medics.
WITNESSES DESCRIBE DAYLIGHT HORROR
The BBC reported the hotel was understood to be housing asylum seekers.
A witness named John said he came down from the hotel to see reception covered in blood and one person who had been stabbed.
"I went down to the entrance and shouted at him and told him to stay calm and I will call for help," he said.
He then saw another man who was "fighting for his life".
Local witness Craig Milroy, who works in an office nearby, told the UK Press Association he saw a man lying on the ground and four people taken away by medics.
"I saw a man lying on the ground, of African descent, with no shoes on. He was on the ground with someone holding his side – I don't know if it was a bullet wound, a stab wound, or what it was.
"After that, we saw commotion, ambulances further up and we saw armed police all running into the hotel next to the Society Room.
"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."
Another witness, who gave her name as Louisa, told Sky News she 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'," she added.
"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."
British Prime Minister Boris Johnson said he was "deeply saddened by the terrible incident in Glasgow" and his thoughts were with "all the victims and their families".
UK Home Secretary Priti Patel said: "Deeply alarming reports coming from Glasgow. Please follow police advice and avoid the area. Thoughts are with the emergency services as they continue to respond to this incident."
