Hernandez was injured during Mexico's 0-0 draw with Honduras in Houston on Wednesday, a warm-up for both teams for the tournament in the United States which kicks off next Tuesday.
The 27-year-old Manchester United forward, who spent last season on loan at Real Madrid, collided with defender Brayan Beckeles five minutes before halftime and was immediately substituted.
"Javier Hernandez underwent a successful operation this morning... He had two plates inserted in his right collarbone fixed with six screws," Mexico team doctor Gerardo Aguiar said in an FMF statement.
"The prognosis is quite acceptable with good expectations for a quick recovery (period) which we hope will be in four weeks."
Coach Miguel Herrera called up Javier Orozco of Mexican champions Santos Laguna to take Hernandez's place with the striker saying he was sorry his chance had come due to a teram mate's misfortune.
"It's a shame it had to be this way, with an injury to 'Chicharito' who is a standout player in the national team," Orozco told Televisa.
"But I'll make the most of my chance... It's important to come back (home) with the Cup because it's an obligation to win it."
Hernandez is the second player to withdraw from Hererra's squad after defender Hector Moreno, who has a toe injury.
He has notched 40 goals in 73 appearances for his country and will be a significant loss as they bid for a seventh title at the July 7-26 tournament in Canada and the United States.
Mexico start their Group C campaign against Cuba in Chicago on July 9 before matches with Guatemala and Trinidad and Tobago.
(Reporting by Carlos Calvo, additional reporting by Patrick Johnston, writing by Rex Gowar; Editing by John O'Brien and Ken Ferris)
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