The match will be England's final group nine qualification fixture for next year's tournament in Japan and Korea.
"We are delighted to be bringing the senior England team back to Manchester United," FA director of marketing Paul Barber told a news conference.
"Old Trafford is an obvious choice for such an important fixture. It's a fantastic stadium where supporters generate an atmosphere which is second to none," he added.
England last played a fixture at Old Trafford in 1997, when they defeated South Africa 2-1 in a friendly match.
The game is the latest to be allocated to a regional city while Wembley, England's national stadium, is being rebuilt.
"As part of our plans to take England on the road over the next three years, we are determined to provide as many people around the country as possible with an opportunity to see the national team in action," Barber said. "Old Trafford maximises that potential."
England play Finland in another World Cup qualifier at Liverpool's Anfield on March 24.
Newcastle United's St James' Park will host the penultimate qualifier against Albania in September.
Leeds United's Elland Road, Totenham Hotspur's White Hart Lane and Derby County's Pride Park are all expected to stage friendlies until the new Wembley is completed.
Reuters
Old Trafford will host England's World Cup qualifier with Greece on October 6, the Football Association announced on Friday.
