He has denied any wrongdoing.
Chen's family is suspected of sending at least T$1 billion ($30.4m) to Japan, the US, the Cayman Islands, Singapore and Switzerland, among other places, Taiwan newspapers said, citing the Supreme Court prosecutor's office.
Prior to his arrest Chen had said the prosecution moves against him were linked to attempts by his successor, Ma Ying-jeou, to placate China following violent protests last week against a visiting Chinese envoy.
Raising his hands in the air to show the media his handcuffs as he left the prosecutor's office on Tuesday, Chen declared: "Long live Taiwanese democracy! Long live Taiwanese independence!"
Earlier dozens of Chen's supporters had gathered outside the prosecutor's offices during the questioning, with riot police deployed to prevent them from entering the building.
Chen, a strong advocate of independence from Beijing, was replaced by Ma, who became Taiwan's president earlier this year on pledges to improve the ailing economy amid broader discontent over Chen, whose frequent prods at China alienated not only Beijing but also Taiwan's important ally, the US.
On Wednesday officials in Beijing confirmed they "had noted" Chen's arrest, but gave no opinion on the allegations against him.
However, a spokeswoman for the mainland government's Taiwan Affairs Office rejected Chen's suggestion that his detention was linked to Ma's efforts to improve ties between the two sides.
Beijing has claimed self-ruled Taiwan as its territory since the end of the Chinese civil war in 1949 and has pledged to eventually return the island to mainland rule, by force if necessary.