Holden, 25, sustained a deep cut in Saturday's 1-0 defeat by Manchester United after a tackle that defender Jonny Evans was shown a red card for.
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As well as missing the Gold Cup, the tournament for countries from North and Central America and the Caribbean, Holden will also have to sit out Bolton's trip to Wembley next month for an FA Cup semi-final against Stoke City.
"First and foremost our main concern is for Stuart and his recovery. He will get all the time and support that he needs," Bolton manager Owen Coyle said on the club's website.
"He has such desire, strength of character and a winning mentality, and he will draw on all those attributes in this rehabilitation."
Influential midfielder Holden was taken off on a stretcher after the tackle which Evans has apologised for.
"Just had a sincere phone call from Jonny Evans wishing me the best in my recovery, def wasn't intentional, just unfortunate part of the game," Holden wrote on Twitter.
Holden was a member of the U.S. squad that reached the second round of last year's World Cup in South Africa.
