The 23-year-old has a knee injury which was confirmed by the Argentinian Football Association.
"Manuel Lanzini was discharged from the squad to play in the Olympic Games in Rio due to injury," an AFA statement confirmed.
"The West Ham man will stay in Miami, from where he will depart directly for London.
"The necessary procedures have been put in place to call up Boca Juniors player Cristian Pavon, who is part of the reserves for the initial list, as his replacement".