Rodriguez landed awkwardly in the first half and was in tears as he was stretchered off the pitch at the Etihad.
Saints are waiting to find out the full extent of the injury, but manager Mauricio Pochettino revealed that early signs were worrying for the striker, who was pushing for a place in Roy Hodgson's squad.
"To be honest, it is not looking good," Pochettino said.
"I can't really know what is wrong with him or when I am going to see him again in a Southampton shirt. We need to analyse him today and tomorrow and know the exact nature of his injury."
The Saints boss admitted it was "possible" that Rodriguez had suffered ligament damage, which could sideline him for the tournament in June.
Hodgson, who handed Rodriguez his only cap in last November's friendly defeat against Chile, was watching the match from the stands.