The information had been leaked to Balfour Beatty by a third party. The council called in Lothian and Borders Police last week and they have started a formal investigation into the allegations.
Balfour Beatty made it clear that it and the employee concerned were unwitting victims of attempted malpractice.
It said: 'The decision to withdraw follows the company's inadvertent receipt from a third party of material sensitive to the bidding process. The fact and circumstances of the receipt of the material were disclosed to the council at the earliest possible opportunity.'
The council said it believed the incident was the work of a `rogue' employee rather than a general systems failure.
The official is understood to have been sacked from the council without benefits.
Council leader Donald Anderson said: 'The integrity of the council is paramount and we will act ruthlessly and swiftly with anyone who damages this.'
A police spokeswoman said: 'We received a complaint and are investigating.'
Bidders were hoping to hear later this month which had won the job with work starting on the first schools next Easter. The final school was due to have been finished by June 2009. Council leaders are now resigned to work not beginning until 2007.