WASHINGTON—The White House signed off on the use of a government jet to take Treasury Secretary Steven Mnuchin and his wife to an event last month in Louisville, Ky., according to a Treasury Department official, prompting a review by the agency’s watchdog.

Treasury considered several travel options, including a commercial flight, before submitting the request for a military aircraft, said Drew Maloney, Treasury’s assistant secretary for legislative affairs, in a letter to Sen. Ron Wyden (D., Ore.) this week obtained by The...