The Grand Central Hotal at the station was also evacuated as a result, with guests left standing in the street.
Network Rail has now confirmed that the station has reopened to the public.
Commuters reported being told over the station's public announcement system just after 8.10am to leave the building immediately due to an "emergency".
Debris from gale force winds smashed part of the glass roof at the station, causing shattered glass to fall to the floor.
There have been no reports of any injuries.
A spokesperson for Police Scotland said: "Glasgow Central train station is closing temporarily due to safety concerns regarding current weather conditions."
An advertising board which came loose also caused Union Street to be closed.
At Port Glasgow Station in Inverclyde, part of the station roof was blown onto the tracks.
Winds reached 63mph in Glasgow.
John Hutchinson, a senior forecaster with MeteoGroup, the weather division of the Press Association, said winds were expected to reduce in strength this afternoon.
He said: "We have a band of heavy rain with some much colder air coming in behind that, especially across northern areas, so there will be snow showers.
"The colder air is flooding down from the north."