Earlier this month, she lost her presidential immunity and was dismissed from her post when the constitutional court upheld a decision by parliament to impeach her.
Ms Park is accused of allowing her close friend Choi Soon-sil to allegedly extort money from big firms.
Ms Park has denied the allegations.
The former president apologised to the public last week, before being questioning by authorities for 14 hours.
"The case is very grave as the suspect has demonstrated acts of abuse of power by making companies give money and infringing on the freedom of corporate management by using powerful position and authority as president," prosecutors said in a statement on Monday.
The prosecutors argue that evidence like computer hard drives might be destroyed if Ms Park is not arrested, the BBC's Stephen Evans in Seoul says.
Ms Choi has been charged with bribery and corruption and is already on trial.