"'Chicharito' suffered a fractured right hand falling down the stairs in his flat last night," said Leverkusen in a statement.
"Hernandez was successfully operated on this morning."
Injury means both Hernandez and Leverkusen captain Lars Bender have been ruled out of Saturday's German league match at Borussia Moenchengladbach, the club's first of the season.
The pair are expected to be sidelined for the next fortnight.
Bender suffered an ankle injury playing for Germany in the men's final of the Rio de Janeiro Olympic Games last Saturday, when the Germans lost to Brazil on penalties.
His injury was confirmed by an MRI scan by his club in Cologne on Tuesday morning after his return from Brazil.
The 28-year-old Hernandez joined Leverkusen from Manchester United in August 2015 and was the club's top-scorer in his first season in Germany with 17 goals in the Bundesliga.
Bender has won 19 caps for Germany and has made 174 league appearances for Leverkusen since joining in 2009.
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