The teenager’s new deal will see him remain at Old Trafford until June 2028.
“When I joined this incredible club, I dreamt of achieving my debut, playing at Old Trafford, scoring my first goal and winning trophies with this badge on my chest,” Garnacho said in a statement.
“I feel very proud and emotional to have experienced these moments already, together with my family who have supported me every step of the way.
“We are all humbled to have this chance to continue our journey at Manchester United and I have already begun to work on achieving the next set of targets and ambitions.
“The manager and his coaching staff have helped me to improve in every way, and with their support, I am developing each day to help the team to be successful.
“I am relishing the future and can’t wait to create more special memories with this group, in front of our amazing supporters.”
Garnacho is thought to have asked to join up with his international teammates for the tournament which Argentina will host between May 20 and June 11.
Asked whether Garnacho would join up with Argentina’s Under 20s, Ten Hag said: “No, we don’t release him.”
The winger has been sidelined with an ankle problem sustained in United’s 0-0 draw against Southampton on March 12.
Speaking after Thursday’s 2-2 draw at Tottenham, Ten Hag said Garnacho would step up his comeback on Friday.
“He will return tomorrow in team training, partial, and then we have to see when he can return totally in the team training and then back into games,” Ten Hag added.
Garnacho has registered four goals and five assists from 29 appearances across all competitions this season.