Henriquez had been hoping to represent his country at the South American Under-20 Championship in Argentina next month, but says United will not let him go.
The Red Devils would prefer the 18-year-old to gain experience of playing in the Premier League and have lined up a short-term deal with Wigan.
Henriquez said in the Daily Mirror: "I asked repeatedly to go (and play for Chile) and showed desire to do so. But they want me to go to Wigan and keep playing in the Premier League.
"I would never say no to Chile. It would be a serious mistake, but United are not letting me go."
Henriquez has not yet broken into the United side but is expected to be granted opportunities at Wigan, especially with Arouna Kone going to the Africa Cup of Nations next month.
He added: "I already talked to the manager Roberto Martinez and he told me that I would have more chances.
"His idea is to have me as a substitute for Kone. It will then depend on me taking advantage of them."