Nobody was hurt when the derelict property collapsed at Pen Y Bryn on Sunday at about 17:00 GMT.
The A5152 road was shut between Tenters Square and Chapel Street to allow for the demolition overnight.
"It's quite scary really as it was a major collapse... on to the footway and the road", said Wrexham council leader Mark Pritchard.
He said an investigation was under way to understand what happened to cause the privately-owned building to collapse.
He thanked contractors for working through the night to complete the demolition of the rest of the building.
"It's so important to find out the reason why it did collapse," he said.
CCTV footage confirmed no pedestrians were in the area at the time, said North Wales Police.
A police helicopter used special heat-seeking equipment to search the site while North Wales Fire and Rescue Service also used sound equipment to check no one was beneath the rubble.