Three engines from Merseyside Fire and Rescue Service dealt with the blaze which broke out on a pile of plywood on the first floor of the building.
Three men were assessed by paramedics and one taken to the Royal Hospital for further attention.
Merseyside Fire and Rescue Service said they will be carrying out an investigation to determine the cause of the fire.
A spokeswoman from Carillion told the Liverpool Echo that around 1,000 workers were evacuated from the site.
She said: “Workers were evacuated within minutes at about half one because of a small fire. Everyone was able to go back to the site about an hour later.
“The fire service attended and the cause is still being investigated.
“One person was taken to hospital for a check.”
