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.
Prosecutors said on Monday that they had "concluded that it is in line with the laws and principles to seek an arrest warrant".
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.
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