Aguerd limped off after 23 minutes of the Hammers' pre-season friendly match against Rangers at Ibrox, which they lost 3-1
The 26-year-old joined the Hammers from Ligue 1 side Rennes for £30m.
The Hammers added that the Morocco defender would now "continue his rehabilitation at Rush Green with the club's medical team".
Aguerd had made his debut in the previous match against Reading.
The transfer fee for Aguerd, who has 25 caps for Morocco, is the fourth-highest paid by West Ham, behind those for Sebastien Haller, Felipe Anderson and Kurt Zouma.
West Ham will begin their Premier League campaign at home to champions Manchester City on Sunday, 7 August.
-- Courtesy of BBC Sport