But Klopp said his captain could be back for Liverpool's final games of the season.
"It (Henderson's injury) is serious, but it's not that serious that there's no hope for us for maybe the last one or two games, and of course there's hope for the European Championship," the German told the club's website (www.liverpoolfc.com).
"We will do everything for him, for us, that he's back in the race as soon as possible. We also have to wait for how each day and see how he does."
England face Russia, Slovakia and Wales in Group B of the 24-team tournament and coach Roy Hodgson will name his squad on May 12.
(Reporting by Simon Jennings in Bengaluru, Editing by Ed Osmond)
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