The 23-year-old Nigeria international travelled to Portugal for the club's UEFA Europa League clash against Vitoria Guimaraes last Thursday but was unable to play after feeling severe discomfort.
Tests showed that the midfielder was suffering with enthesopathy in the adductor muscle of his left leg, which requires surgery to correct.
Nosa, who has scored once in 10 appearances for Pepe Mel's side this term, is not expected to return to action until the new year.
He will subsequently be unavailable for Nigeria for their crucial FIFA World Cup qualifier match against Ethiopia on Saturday, having come off the bench in their 2-1 first-leg victory.
Betis sit bottom of La Liga with nine points from their opening 13 league fixtures and were beaten 4-1 by champions Barcelona on Sunday.
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