The England international had netted five goals in four games heading into Saturday's clash at Manchester City, where he was forced off midway through the first half.
Rodriguez appeared to sustain a serious injury to his right knee after landing awkwardly, resulting in him being taken from the field on a stretcher.
The full extent of the injury will not be known until the swelling subsides, but Pochettino fears the worse for the 24-year-old.
"To be completely honest, it is not looking good," the Saints boss said after the 4-1 defeat in Manchester.
"We need to assess him today and tomorrow, but it is not looking good. It is not going to be good for him, not good for the team.
"I can't really know exactly what is wrong with him and when I am going to see him again in a Southampton shirt.
"We need to analyse him today and tomorrow to know the exact reality of his injury.
"All the players are really affected, not just about the result and the refereeing decisions but more than anything the doubt about how severe his injury is."
Asked if he thought it was ligament damage, Pochettino said: "It is possible but at the moment I can't really say anything at all because we have not analysed him yet."
If Rodriguez has suffered anterior cruciate ligament damage, he will face at least six months on the sidelines, with the injury witnessed first-hand by England boss Roy Hodgson.
The attacker made his England debut against Chile in November and was part of the squad for the recent friendly with Denmark, putting him in the running for a World Cup spot that may well have been cruelly taken away from him.
Rodriguez was given a standing ovation by both sets of fans as he left the field, while there were messages of support on Twitter from the likes of Gary Lineker, Joey Barton and Dietmar Hamann.
"Gutted for Jay Rodriguez," former Germany international Hamann said. "What a fantastic season he has had. Will weaken England if he's out the World Cup."
England international Theo Walcott will miss this summer's tournament in Brazil with an anterior cruciate ligament injury, which has also struck down Colombia striker Radamel Falcao and Spain goalkeeper Victor Valdes recently.