The former Manchester United striker will not be adding to his 22-goal haul for the season in Bayer Leverkusen's latest match on Saturday
Hernandez hit his 22nd goal of the season, from the penalty spot, to put Leverkusen ahead in their DFB-Pokal quarter-final with Werder Bremen on Tuesday, but was later substituted.
Bremen came back to win 3-1 at the BayArena thanks to goals from Santiago Garcia, Claudio Pizzaro and Florian Grillitsch, while Bayer had Wendell sent off.
Bayer have revealed the Mexico international suffered a "small fibre muscle tear of the left glutes" in the game.
Hernandez will now miss the trip to Darmstadt, with the club writing on Twitter: "We're hoping for a speedy recovery!"
The 27-year-old striker has won the Bundesliga's player of the month award three times in a row, scoring 10 goals in his last nine matches.