The case is at the centre of contempt proceedings against Prime Minister Yousuf Raza Gilani, who is accused of failing to pursue the allegations.
The government has argued that Mr Zardari has presidential immunity. He says the case is politically motivated.
But the court has said a compliance report must be filed by 21 March.
The Supreme Court earlier adjourned a contempt hearing against the prime minister to 21 March as well, saying that Mr Gilani must either file a statement or testify personally that day.
Correspondents say that by ensuring that both cases are heard on the same day, the court has effectively narrowed the legal options of the prime minister.
Mr Gilani is being tried for contempt because he has refused to write a letter to the Swiss authorities despite a Supreme Court order which overturned an amnesty on corruption cases said to be politically motivated.
The BBC’s M Ilyas Khan in Islamabad says Thursday’s court order is likely to further heighten the tensions between the government and the judiciary.
Many in Pakistan wonder whether this is a power struggle between two state institutions or a battle to ensure the rule of law, our correspondent says.
Analysts say the court and the government are locked in a power struggle over who is the final arbiter of the rule of law.