Han was one of nine people the police said they questioned over their attendance at a Cabinet meeting Yoon held shortly before he declared martial law on December 3, Yonhap news agency reported.
This marks the first time Han has been known to have undergone questioning as a suspect in the probe.
"Of the 12 people who attended the Cabinet meeting, we questioned nine people, excluding President Yoon Suk Yeol, former Defence Minister Kim Yong-hyun and Unification Minister Kim Yung-ho," a police official said.
"Despite the police's continued requests for appearance, the unification minister appeared before the prosecution and underwent questioning there," the official said.
A senior official at the Prime Minister's Office told reporters the questioning took place "before the transition to acting president," suggesting it was on or before Saturday.
Han, as prime minister, took over as acting president after Yoon was impeached by the National Assembly and suspended from duty on Saturday.
"(Han) engaged fully and faithfully in the investigation," the official said.
Police have teamed up with the Corruption Investigation Office for High-ranking Officials and the Defence ministry to conduct a joint investigation into charges that Yoon and others incited an insurrection and abused their power in imposing martial law and sending troops to the National Assembly to allegedly block lawmakers from repealing the decree.
The prosecution has launched a parallel investigation into the case, but they transferred their probe of Yoon and former Interior Minister Lee Sang-min to the joint probe team earlier this week.