Scottish police also promised further updates in a tweet Monday.
Speaking to the BBC earlier Monday, Superintendent Stuart Carroll said itappeared the "bin lorry" had struck one pedestrian before going up onto the sidewalk and colliding with a number of others.
Police said the truck crashed at the Millennium Hotel Glasgow at George Square.
Carroll said "at least seven" people had been seriously injured. "The driver has also been taken to hospital where he is receiving treatment," Carroll said.
"For now it does not look to be either a criminal or deliberate act," he said.
Assistant Chief Constable Wayne Mawson said investigations into the circumstances of the "tragic incident" were ongoing.
"We can however confirm that this is not a terrorism-related incident," he said.
Police earlier told CNN the incident was being investigated as a road accident.
A Glasgow police spokesperson said the incident occurred just after 2:30 p.m. (9:30 a.m. ET) Monday.
Diversions and road closures are in place and police have asked people to avoid the area.
British Prime Minister David Cameron said on Twitter that he was being kept "fully briefed" on the incident.
"My thoughts are with the families of those involved & emergency services," Cameron said.
First Minister of Scotland Nicola Sturgeon, said her thoughts were with "everyone involved in dreadful #GeorgeSquare incident."