The City defender will be monitored regularly with a view to returning to camp as soon as possible.
Greenwood was selected alongside seven other members of Gareth Taylor's squad to take part in a series of international friendlies against Belgium, the Netherlands and Switzerland across June.
The matches are in preparation for this summer’s European Championships, which are being held across England next month.
A City-focused match report on each encounter will be available to view on mancity.com and the official Man City app once the action has concluded.
Everyone at the Club would like to wish Alex a speedy recovery.