Cables and equipment were ransacked on the first floor of the Energy Centre building, which damaged management systems and control operations.
Security officials on the site discovered the damage last Thursday and immediately reported it to Bovis management.
A project insider said the damage was carried out in a zone that was open only to workers with security clearance.
He said: "It was clear from the extent of the vandalism that it was a deliberate act – specific wires had been cut to cause maximum upheaval and damage."
He said Bovis Lend Lease had begun an investigation to identify the culprits.
The project insider added that, as there were more than 1200 workers on the project, many of whom could have entered the permit-only area, no one subcontractor was under scrutiny.
This is no accident; wires were cut to cause maximum damage
White City project insider
The types of wires that had been cut included building temperature and security controls that could affect systems throughout the whole building and not just the first floor, according to the insider.
"To damage these main sets of controls is no accident; they are very difficult to repair and there must be well over £10,000 worth of damage," he said.
The motive for the sabotage is unclear, but the insider said that there are many workers who are angry at the amount of hiring and firing on the project.
He said: "There is quite a lot of agency labour on the scheme, as well as immigrants, and men that get laid off or are being brought to the project on a week on, week off basis have been getting very angry at the way they have been treated. This could be the reason."
Tony Wilson, the BBC project manager for the site, was out of the country when Building contacted him, and was unaware of the incident. Wilson said he would investigate the matter.