New North East Wales offices for the union Unite are currently being built on the site of a former electronics store on King’s Street in the town.
It is believed the JCB telehandler toppled over shortly after 3pm.
An eye witness told local news site Wrexham.com: “It fell about 15 minutes ago, and the whole of our building shook, it was about two feet from smashing into a car parked at the side of the site.
“The guy crawled out pretty shook up.
“I think everyone came out safe though, and all of the beams it was carrying seem to have avoided making any damage to anything apart from their temporary perimeter fencing.”