"I deeply apologize to the citizens, I will fully cooperate with the investigation," she said outside the prosecutors' offices in Seoul.
Park is being investigated over her involvement in a scandal that has roiled South Korean politics for months and ended her presidency on March 10.
Prosecutors can hold suspects for questioning for up to 48 hours without a warrant. It's possible she could be charged.
The now ex-President's problems began in October, when revelations emerged about the influence her confidante and unofficial adviser Choi Soon-sil exerted at the top of South Korean politics.
Despite never holding an official position, Choi was given advance access to presidential speeches and other documents. She is currently facing charges of abuse of power and fraud
for allegedly using her relationship with Park to force major South Korean companies to donate millions of dollars to two foundations believed to have been set up by Choi.
The scandal has engulfed the country's largest company, Samsung, whose de facto leader Lee Jae-yong was arrested in February on charges of bribery and embezzlement
Choi, Lee and Samsung all deny the allegations.
Earlier this month, the Constitutional Court affirmed a 234 to 56 vote by lawmakers in December to impeach Park. Judges upheld the impeachment on the grounds that Park had abused her authority in helping Choi raise donations from the companies.
'Truth will come out'
Park left the Blue House -- South Korea's seat of government and her childhood home when her father, strongman leader Park Chung-hee, was in power -- on March 12.
She said she was "sorry that I couldn't fulfill my duty as President until the end," in a statement read on her behalf by Congressman Min Kyung-wook to crowds of supporters outside Park's private residence in Seoul's Gangnam district.
"I thank people who have supported and believed in me," Park's statement said. "It will take time, but I believe that truth will definitely come out."
That process will begin this week. Park has promised to cooperate with prosecutors, who may soon seek to indict her and prevent her from leaving the country.
An election for her replacement will be held on May 9