San Diego's Snapdragon Stadium will host the friendly on 26 July (AEDT).
Wrexham, which this month signed former United goalkeeper Ben Foster, are pushing for promotion from the National League.
It sits three points clear of Notts County, while it also reached the fourth round of the FA Cup, losing to Sheffield United, which has gone on to reach the semi-finals.
The Welsh club were bought by Hollywood A-listers Reynolds and McElhenney in 2020.
"We're looking forward to being able to play in the United States for the first time in the club's history," said Wrexham manager Phil Parkinson.
Wrexham last faced United in an FA Cup tie in 1995. The Red Devils' team will be mainly made up of academy players.
