Paul Ceglia says he gave Mr Zuckerberg $1,000 (£629) in 2003 to help set up Facebook and that a deal was signed.
Facebook says the document is a fake and wants the case to be dismissed.
Mr Ceglia's lawyers have been asked to submit expert reports on the contract within two months.
Magistrate Judge Leslie Foschio also said that Mr Ceglia's lawyers would be able to question Facebook's own experts about the two-page document.
While Mr Ceglia, of Buffalo, New York, says the contract entitles him to half-ownership of Facebook, Mr Zuckerberg counters that he had not conceived of the social network at the time.
Facebook's lawyers say Mr Ceglia and Mr Zuckerberg signed a contract in 2003 to develop street-mapping software. They claim that Mr Ceglia subsequently doctored the document to insert Facebook references.
In addition to not being able to question Mr Zuckerberg at this stage, Judge Foschio also refused to allow Mr Ceglia's lawyers access to Mr Zuckerberg's computers from 2003.