The 18-year-old joined the Old Trafford side in August 2012, but has yet to make his first-team debut after finding himself behind the likes of Robin van Persie and Chicharito in the pecking order.
Latics boss Roberto Martinez has expressed delight at the short-term capture of the Chile international, who could make his debut in Saturday's FA Cup clash with Bournemouth.
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“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.”
Henriquez, who will wear the number 11 shirt at the DW Stadium, also revealed his excitement at the prospect of lining up for Wigan.
“This is a fantastic opportunity for me and I am really excited after the manager has given this chance for me to prove myself. Now I need to work to try and earn my place in the team," he said.
The Santiago-born forward made his full international debut in November, replacing Alexis Sanchez in a defeat to Serbia and going on to net his first goal.