SEOUL—A day after declaring martial law, South Korea’s president is now facing the prospect of impeachment, creating more political instability for a close U.S. ally and prompting the resignation of the country’s defense minister.

The South Korean Parliament has submitted a motion to vote on removing the conservative Yoon Suk Yeol by Friday or Saturday, opposition lawmakers said. To do so, they will need a two-thirds backing at the country’s unicameral, 300-seat National Assembly.