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Beckham was substituted in the 33rd minute of the Superliga final against Mexican team Pachuca after a challenge with Fernando Salazar.
The former England captain received treatment to his right knee and limped off the field. He watched the rest of the second half from the bench.
A Galaxy spokesman said Beckham, who has struggled with an ankle injury in recent months, had suffered a sprain to his right knee.
Photograph: Getty Images