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.
"A large amount of evidence has been collected so far but the accused is denying most of the charges, and there is a risk of destroying evidence in the future," it said.
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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.
Two former army-backed leaders who ruled in the 1980s and 1990s - Chun Doo-Hwan and Roh Tae-Woo - both served jail terms for charges including bribery after they retired.
Park was impeached by parliament in December, as the scandal coupled with mounting economic and social frustrations to trigger huge candlelit demonstrations, and the Constitutional Court later upheld the decision.
Watch: South Korea's Park leaves after 14-hour interrogation
New election
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.
Park grew up in the Blue House, with the first family treated as royalty by some supporters and Park dubbed the young "princess" - a nickname that endured for decades.
The assassinations of both her parents five years apart in the 1970s only further fanned sympathy for her.
After her mother was murdered by a Korean-Japanese believed to have been acting on Pyongyang's orders, Park assumed the role of first lady until her father was killed by his own security chief in 1979.
She was elected in her own right in 2012, largely thanks to a bedrock of support among older, conservative voters who benefited from rapid economic growth under her father's rule.
Even as her approval ratings plunged to record lows, some remained loyal.
Hundreds of flag-waving supporters gathered near her home in southern Seoul to welcome her back after she underwent a marathon interrogation session lasting more than 21 hours at the prosecutors' office last week.
Smiling broadly, she nodded at them on arrival and entered the house without answering questions from reporters.
Park has repeatedly apologised for the upset caused by the scandal but not admitted any wrongdoing, blamed Choi for abusing their friendship.
An election to choose her successor will be held on May 9 with Moon Jae-In, her rival in 2012 and a former leader of the main liberal opposition Democratic Party, leading polls by large margins.
