Yingluck fled the country last August to avoid being jailed over a rice subsidy scheme that ran up losses in the billions of dollars. She has denied wrongdoing and said the trial was politically motivated.
The Supreme Court sentenced her in absentia to five years’ jail last September.
Prayuth said the request was a necessary procedure between the two countries which share an extradition treaty.
“We cannot go and arrest people abroad so it is up to that country to arrest and send (her) to us,” Prayuth said.
Yingluck and her brother, ousted former prime minister Thaksin Shinawatra, have been at the center of a power struggle that has dominated Thai politics for more than a decade, pitting traditional royalist and the military elite against the Shinawatra family and their supporters in the rural north and northeast.