The court gave Prime Minister Raja Pervez Ashraf until November 14 to submit the request, threatening to charge him with contempt of court or face disqualification if he did not comply.
The case has fuelled tensions in a long-running standoff between the government and the judiciary. Ashraf's predecessor, Yusuf Raza Gilani, was declared in contempt of court in June over the same issue and disqualified from holding the post of prime minister.
If Ashraf is disqualified, the ruling Pakistan People's Party can simply nominate a new prime minister since it has a comfortable majority in parliament.
But any prolonged political instability would further distract an unpopular government which has failed to tackle a wide range of issues, from a Taliban insurgency to crippling power cuts.
Thousands of corruption cases were thrown out in 2007 by an amnesty law passed under former military president Pervez Musharraf, paving the way for a return to civilian rule.
Two years, later the Supreme Court ruled that agreement illegal, and ordered the reopening of money laundering cases against Zardari that involved Swiss bank accounts.
"Now the ball is in the Swiss court and it's up to Swiss authorities if they want to immediately re-open the cases, or simply bury the case altogether," said Babar Sattar, a legal commentator.
Swiss judicial authorities began investigating allegations in the late 1990s that Zardari, and his late wife, former Prime Minister Benazir Bhutto, had taken kickbacks from Swiss cargo inspection companies and channelled some $12 million via offshore companies into Swiss accounts.
Swiss authorities said that in 2008 the Pakistani government dropped all related cases it had initiated in Switzerland after Bhutto's party won an election and Zardari become president.
A Swiss prosecutor told Reuters in 2010 that Switzerland would not reopen the case against Zardari as long as he enjoyed presidential immunity in Pakistan, and if he no longer had immunity in Pakistan, he should be tried there.