The friendly is part of the 2014 International Champions Cup and continues United's push to build the club's brand in the United States.
United and Real Madrid last met in the 2012-13 season, with the Spaniards winning 3-2 on aggregate in the Champions League last 16, and the teams could still play each other in this season's competition.
The match will take place at Michigan Stadium in Ann Arbor, which is known locally as 'The Big House'.
Manchester United group managing director Richard Arnold said: "Playing such strong opposition will be great preparation for David Moyes and his team.
"This will be the team's first ever match in Michigan and playing at the iconic Big House will be a memorable experience for all involved."