Rodriguez, 24, joins Arsenal and former Southampton winger Theo Walcott in missing out on a berth in England's squad because of the same injury.
"Southampton Football Club can confirm that, following his injury on Saturday against Manchester City, Jay Rodriguez has been diagnosed as having suffered a rupture to his anterior cruciate ligament," Southampton said in a statement on Monday.
"This will keep him out of action for six months and regrettably means he will not be fit for selection by the English national team at this summer's FIFA World Cup in Brazil."
Rodriguez had netted 15 league goals and been in fine form for eighth-placed Southampton, who continue to be one of the Premier League's surprise packages and had hoped to have four players in Roy Hodgson's squad.
Rodriguez's strike partner Rickie Lambert and left back Luke Shaw are hoping for the call while midfielder Adam Lallana has impressed so much in his short England career he is now likely to start in Brazil.
Lallana and Rodriguez made their international debuts together in a home friendly loss to Chile in November and while the striker was somewhat upstaged by his club colleague, he still remained in the hunt for a squad place.
Jermain Defoe's decision to move to Toronto FC in Major League Soccer made Rodriguez's chances of going to Brazil look more likely but now he faces an operation in the near future.
Southampton director Les Reed said: "Jay is naturally disappointed, but is determined to get back playing for Saints as soon as possible.
"Jay has asked us to pass on his gratitude to everybody who has shown him their concern and sympathy during the 48-or-so hours since his injury.
"Everyone at the club now wishes Jay well and we will support him, along with his family, to ensure that an international career plays a big part in his future."
Southampton lost 4-1 at City.
