Crews were called to the scene in Jamaica Street at about 17:07. The building engulfed in flames was thought to be a furniture shop.
Police advised people to avoid the area as smoke billowed from the roof of the property.
The Scottish Fire and Rescue Service said it was dealing with a “large, well-developed” blaze.
A funeral home nearby was forced to move bodies to another premises as crews tackled the fire.
At about 21:00, several hours after the blaze began, police said a number of roads in the area would remain shut.
spokeswoman for Scottish Fire and Rescue Service said: “Operations Control mobilised a number of fire engines to the town’s Jamaica Street, where firefighters were met by a large and well developed fire.
“Crews currently remain on the scene working to extinguish the fire.”
Earlier Police Scotland Control Rooms tweeted: “Road closures are in place. For everyone’s safety please stay clear.”
In a post on their Facebook page, Green Oak Funeral Services said that their landlines were unavailable but “all loved ones were being cared for in our Port Glasgow premises”.
Inverclyde Council said road workers were supporting the emergency services.
It tweeted: “A building standard officer is also in attendance to assess building damage and any safety issues. Please support the emergency services and avoid the area and follow any diversions.”