Southampton lost Saturday's game at the Etihad Stadium 4-1, though their primary concern will centre on the condition of striker Rodriguez after he was forced off midway through the first half.
The 24-year-old appeared to badly twist his right knee as he attempted to control a high ball and crumpled in a heap on the turf, immediately signalling for the physio.
Rodriguez was given oxygen and had his leg heavily strapped as he was stretchered off, and his season looks to be over.
It is also likely to end any hopes he had of making England's World Cup squad, having become a contender with 15 goals in his 33 Premier League appearances this season.
When asked of Rodriguez's condition, Southampton manager Mauricio Pochettino said: "To be completely honest, it's not looking good.
"We need to assess him today and tomorrow but it's not looking good for him it's not going to be good for the team.
"All the players are really affected, not just about the result not just about the decisions but more about how severe his injury is."
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