Holden had started Bolton's last two matches and impressed Owen Coyle enough to earn a contract until the end of next season.
"It's disappointing for Stuart because he has come into the team and done ever so well," said Coyle.
"What we do know is he will come back bigger and stronger, but it is sad for him to miss out at this moment in time.
"He's come in with a real hunger and desire to do well for our club, and in the two games he's played, we've seen his quality."
Coyle is hopeful the injury will not damage Holden's prospects of playing in the World Cup, with the United States' opening group game against England on June 12.
"Only time will tell," added Coyle.
"We're erring on the side of six weeks, and if that is the case then he will be capable of playing the last part of the season for us and putting himself in the frame for the World Cup."
With regard to Holden's extended deal, Coyle feels he has already proven himself in the short space of time he has been with Bolton.
The Scot added: "We've already spoken with him and his representative to assure him he will be here for longer because of the belief I have in him, and the quality he has shown since he came to the club.
"When we signed him, within the contract there was the option there to extend it further, which we will do.
"It augurs well for his future and that of the football club."
Holden picked up the injury in a tackle with Manchester City midfielder Nigel de Jong.
De Jong was booked for the challenge, but he insisted there was no malice intended.
"Such offences are part of football," he said on the Dutch FA's website. "I went for the ball and got the opponent at the end.
"I had no evil intent. If the ball is between me and the opponent, you have to go in full. If you do not then the opponent takes you.
"And if you're scared in a game you get injured yourself."
USA v Mexico Progress Furthest Progress the Furthest: USA 5/6