Park, 65, had her removal from office confirmed by the country's top court earlier this month, ending her executive immunity, and her prosecution has been a key demand of the millions of people who took to the streets to protest against her.
The former president is accused of multiple offences including bribery, leaking government information, and abuse of power in the scandal.
"The accused abused her enormous power and status as president to receive bribes from companies or to infringe upon the rights to freedom of corporate management and leaked important confidential information on state affairs. These are grave issues," the prosecutors said in a statement.
Choi Soon-Sil, Park's secret confidante at the heart of the scandal, is already on trial for forcing top local firms to "donate" nearly $70 million to non-profit foundations she allegedly used for personal gain.
Prosecutors said it would be "counter to the principle of fairness" if Park was not arrested.
If Seoul Central District Court approves the warrant, Park will become the third former leader to be arrested over corruption in Asia's fourth-largest economy, where politics and big business have long been closely tied.
Park has been named as Choi's accomplice for allegedly offering governmental favours to top businessmen who enriched her friend, including Samsung heir Lee Jae-Yong, who was arrested last month and charged with bribery last month.
She is also accused of letting Choi, a high school graduate with no title or security clearance, handle a wide range of state affairs including nomination of top officials.
Park, daughter of late dictator Park Chung-Hee, is also said to have ordered aides to leak secret state files to Choi, and to have cracked down on thousands of artists who had voiced criticisms of her or her father's iron-fisted rule from 1961 to 1979.
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