The 21-year-old Uruguay international midfielder, missed Sunday's 2-2 draw against Fulham after being treated in hospital for a "dead leg" which resulted in severe swelling in the player's thigh.
He has also been forced to withdraw from Uruguay's squad for their upcoming World Cup qualifiers against Argentina and Bolivia.
Ramirez, who joined the Saints from Bologna in August for 12 million pounds ($19.23 million) could miss the club's next four league matches against West Ham United, Tottenham Hotspur, West Bromwich Albion and Swansea City.
Saints manager Nigel Adkins told reporters after the Fulham match that the injury "was quite a serious one".
"The muscle swelled up very much because there was nowhere for the blood to go, so there was a lot of pressure on his thigh," Atkins said.
"He has had to have a couple of days in hospital to try and relieve the pressure, so obviously he is not going to go and join the Uruguayan team over the international break."
Ramirez has made three appearances for Southampton since joining on transfer deadline day and scored his first goal in the 3-1 defeat at Everton last week.
The club are currently 17th in the 20-team Premier League having won one, drawn one and lost the other five of their opening seven league matches following their return to the top flight after a seven-year absence.