The 22-year-old is currently undergoing treatment after his cancer returned. Alvarez initially had a tumour removed in December 2016, but has been sidelined again by the disease.
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He played just two months after having the tumour removed, returning to action in February, and now Bilbao expect him to be out for at least three months.
His team-mates at the club have backed the Spain Under-21 international, and posed for a squad photo with their heads shaved.
Midfielder Benat is almost unrecognisable in the picture, having chopped off his long locks for his team-mate.
Alvarez also shared a similar image of the squad’s new look on his Instagram, accompanied by the caption “This family is a crazy thing!”