The petition also asked for new elections to be called within 60 days.
The Zimbabwe Election Commission declared last week that Mugabe defeated Tsvangirai 61 percent to 34 percent.
The prime minister's party, Movement for Democratic Change, has accused the commission of rigging the election to favor Mugabe's Zanu-PF party.
Douglas Mwonzora, the MDC spokesman, outlined 15 reasons why the vote should be thrown out, including some voters being bribed to vote for a particular candidate and lack of professionalism by the commission.
Zanu-PF youth leader Tafadzwa Mugwadi said he thought the court challenge would fail because the election was peaceful. He charged the challenge was generated by "an instruction" from the United States, England, Canada and Australia.
If the case is dismissed, Mugabe will be sworn within 48 hours.