The move, which was expected, will see 18-year-old Chilean Henriquez join Wigan for the rest of the current season.
Henriquez was brought in by United last summer from Universidad de Chile and has already made his full international debut.
Wigan are in a familiar position of battling to avoid relegation from the Barclays Premier League and lost 4-0 to United on Tuesday.
Latics boss Roberto Martinez told Wigan's website: "We're really excited about Angelo because he is a very young man with a huge potential; he's a goalscorer with clever movement inside the box and has had a very successful time with his former club Universidad.
"We hope to have a good partnership in terms of allowing Angelo to develop as a footballer and learn of the demands of the English game, because I feel he can bring us something different in the forward line.
"I'm sure the fans will give him a great welcome on Saturday and it will provide him with the perfect opportunity to begin his experiences on the pitch in English football which is very exciting."