His liberal PLDM party - in Moldova's ruling coalition - condemned the move as "purely political" and "a violation of his rights".
He was arrested on Thursday, suspected of involvement in the disappearance of $1bn (Â£646m) from three Moldovan banks.
The scandal has thrown Moldova into economic and political chaos.
In recent weeks thousands of people have protested in the centre of Moldova's capital Chisinau, demanding that the government and top civil servants resign.
The missing money is equivalent to an eighth of the ex-Soviet republic's entire GDP. Moldova is one of Europe's poorest countries.
The scandal caused a rapid fall in the value of the national currency, the leu, hitting Moldovans' living standards.
Mr Filat, leader of the PLDM, was initially detained for 72 hours, accused of theft from the state-run Banca de Economii. Earlier parliament had stripped him of immunity from prosecution. He denies wrongdoing.
Anti-government protesters welcomed his detention. One of their leaders, Renato Usaty, called it "our first victory".
Moldova's central bank has withdrawn the operating licences of Banca de Economii and two other banks - the private Banca Sociala and Unibank.
The scandal erupted in April, when the central bank found that the three banks had lent $1bn to unidentified beneficiaries.
The trail points to a UK-registered company, Fortuna United, which is a limited partnership made up of two Seychelles companies.
Fortuna United is named in a leaked report, by the New York-based corporate investigative agency Kroll, as the firm that is ultimately owed the entire proceeds of the Moldovan fraud.
Businessman Ilan Shor, a former chairman of Banca de Economii, has told prosecutors that Mr Filat received payments from the bank, Moldova's Infotag news agency reports.
Mr Shor denies involvement in a scheme to siphon off money from the banks.
A court has extended the detention of Moldova's former Prime Minister Vlad Filat for 30 days as his possible role in a $1bn banking scam is investigated.