The head of the state-owned bank and at least a dozen other people also face charges.
The suspects are accused of abusing their power by taking or facilitating bribes.
PM Recep Tayyip Erdogan has denounced the investigation as a “dirty operation” against his government.
The controversial arrests began on Tuesday when police launched a series of dawn raids in Istanbul and Ankara.
On Thursday the head of Istanbul’s police was forced from his position, and more than 30 senior police officers have reportedly been sacked.
The corruption investigation has targeted people close to Receo Tayyip Erdogan’s administration.
Baris Guler, the son of Interior Minister Muammer Guler and Kaan Caglayan, son of Economy Minister Zafer Caglayan was among those detained, as is the chief executive of the state-owned Halkbank, Suleyman Aslan.
They were put under formal arrest on Saturday morning.
The son of a third minister – Environment and Urban Planning Minister Erdogan Bayraktar – was among those released after hours of questioning.
Commentators in Turkey report that the arrests and firings reflect a feud within Turkey’s ruling AK Party between those who back Recep Tayyip Erdogan and supporters of Fethullah Gulen, an Islamic scholar living in exile in the US.
Members of Fethullah Gulen’s Hizmet movement are said to hold influential positions in institutions such as the police, the judiciary and the AK Party itself.
Opposition leader Kemal Kilicdaroglu has accused Recep Tayyip Erdogan and his government of trying to cover up the scandal.
Kemal Kilicdaroglu, the leader of the Republican People’s Party, called for ministers implicated in the investigation to be sacked.
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