Economy minister Zafer Caglayan, interior minister Muammer Guler and environment and urban planning minister Erdogan Bayraktar denied any wrongdoing.
Mr Bayraktar gave a television interview in which he urged Mr Erdogan to step down.
Mr Caglayan’s and Mr Guler’s sons, along with the chief executive officer of the state-run Halkbank, are among 24 people held on bribery charges. Mr Bayraktar’s son, Abdullah Oguz, was detained but later released.
Media reports said police have seized $4.5 million (£2.8m) in cash stashed in shoe boxes in the home of the bank’s chief executive, while more than $1m in cash was reportedly found in the home of Mr Guler’s son, Baris.
Mr Erdogan has denounced the corruption probe as a plot by foreign and Turkish forces to thwart Turkey’s growing prosperity and discredit his government ahead of local elections in March. Critics accuse him of becoming increasingly authoritarian, but his government has won three successive elections since 2002 due to a relatively robust economy, a clean image and a promise to fight corruption.
The probe is one of the biggest challenges Mr Erdogan has faced since his Islamic-based party was almost banned in 2008 for allegedly undermining Turkey’s secular constitution. This summer, he also weathered a wave of protests sparked by a development project in a popular Istanbul park.
Wednesday’s resignations came as a surprise. Mr Erdogan was expected to remove ministers implicated in the scandal quietly, through a planned reshuffle to replace three other ministers running for posts as mayors in the March elections.Turkish commentators believe the probe is fallout from a power struggle between Mr Erdogan’s government and an influential US-based Muslim cleric, Fethullah Gulen, whose followers are said to have a strong foothold within Turkey’s police and judiciary. The two men, without naming each other, have been engaged in a war of words since the corruption probe was launched on 17 December.
Mr Gulen has denied being involved in the investigation. He left Turkey in 1999 after being accused of plotting to establish an Islamic state. He was later cleared and allowed to return home, but he has remained in the US, living in Pennsylvania.
In an address to his party’s local leaders, Mr Erdogan distanced himself from the ministers who resigned by stressing his party’s determination to fight corruption.
But he also repeated a claim that his government was the target of an international plot involving the media and “gangs” inside Turkey – a tactic he used during the summer’s protests to deflect criticism.
“There are media institutions, organisations and gangs in Turkey who think of others’ interests rather than their own country’s interests, and are working as spies in a treasonous manner,” Mr Erdogan said.
In a veiled attack on Mr Gulen, he added: “They speak of the Koran and of Allah but are remembered for … plots.”