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.