Reporting from Harare, Supa Mandiwanzira, Al Jazeera's correspondent in Zimbabwe, said: "The Zimbabwe Election Commission was arguing that this case cannot be brought before the high court because it has no jurisdiction over a constitutional body.
"The judge has said it has jurisdiction and he has postponed proceedings to 10am Zimbabwe time [0800GMT]."
Tsvangirai says he won last week's election but the ruling Zanu-PF party of Robert Mugabe, the incumbent president, says there is no clear winner and has called for a run-off vote.
MDC has called for the election commission immediately to publish the results and validate Tsvangirai's claim.
"A mooted presidential run-off ... is a sham," Tsvangirai wrote in a commentary in Monday's issue of the British newspaper The Guardian.
"Our country is on a razor's edge," he said.
He called on South Africa, Britain and the US to step up pressure on Mugabe and his supporters to stand aside.
State media reported on Sunday that Zanu-PF had snubbed an approach from the MDC to form a unity government and was now demanding a complete recount of the presidential vote after detecting irregularities.
The MDC has denied that a unity government was ever on the table.
Mugabe chaired a meeting of Zanu-PF's politburo on Friday and was endorsed to compete in a run-off if neither of the two main contenders wins more than 50 per cent of the presidential vote.
He has ruled without interruption since Zimbabwe gained independence from Britain in 1980, but has lost support amid an economic crisis.
Zimbabwe has the world's highest rate of inflation - more than 100,000 per cent - and about 80 per cent of the work force is without employment.
Source: Al Jazeera and agencies