After South Korea's president and his replacement were both deposed over a failed bid to impose martial law, deepening political turmoil is threatening the country's currency and shaking confidence in its economy.

SEOUL—South Korea’s legislature voted to impeach acting President Han Duck-soo on Friday after he declined to make judicial appointments needed to advance the impeachment of his predecessor, extending the political upheaval that began with a short-lived martial law declaration earlier this month.

Finance Minister Choi Sang-mok is next in line to take on the mantle of the acting presidency, according to South Korean law.