The 21-year-old was the newly-promoted club's marquee acquisition this summer, joining from Serie A outfit Bologna for upwards of £12million and much fanfare.
Ramirez may have only played three matches for his new club but has impressed, scoring one and setting up another.
The attacker missed Saints' last match against Fulham and Uruguay's international fixtures with a dead leg, which manager Nigel Adkins today confirmed will keep him out for a further four weeks.
"I think six weeks (in total) is probably about right, but we'll see how he progresses through the rehab stages," the Saints boss said ahead of Saturday's trip to West Ham, where they will be hoping to add to their four-point haul.
"If the time is from the medical department, it is from the date of original injury.
"He is showing good signs of recovery at this moment of time, but he won't be fit for the weekend.
"He did not travel to Uruguay for the international game. He has still got a dead leg, to use a common phrase, so he will not be available for this weekend.
"We will see how he progresses with rehab over the next period of time."
Tadanari Lee, Jack Cork and Danny Butterfield are also out of contention through injury, while Adkins confirmed Frazer Richardson will also miss the trip to east London.
The right-back, playing in place of the injured Nathaniel Clyne, picked up a thigh complaint minutes into the 2-2 draw with Fulham, a game the Saints boss had hoped to take three points from.
"You need to win your home games," he said. "You need to win your home games and pick up as much as you can away from home.
"We had Fulham the previous time out and obviously we've targeted that game as one to go and win.
"We've picked a point up, but it was a game we wanted to win and in that game we didn't have Gaston or Nathaniel Clyne so there were two players we've invested in in the summer.
"You have seen the signs already from Gaston and the way he has performed that he is going to really excite our supporters.
"He can create goals and score goals so it was disappointing he was not available for us in a game we were looking to win."
While Ramirez remains out, fellow new boy Clyne will almost certainly return to the starting line-up at Upton Park after a dead leg that also forced him out of the England Under-21 squad.
It was possibly a blessing in disguise for the former Crystal Palace full-back after the Young Lions' qualification for Euro 2013 was marred by a mass confrontation on the pitch in Serbia and allegations of racist abuse from the stands.
Tottenham's Danny Rose, on loan at Sunderland, was sent off for his reaction in the aftermath, clearly indicating he felt he had been been racially abused, something the Serbian Football Association have denied.
"They were unsavoury scenes," Adkins said of the matter. "It is something you don't want to see in football.
"I am sure there will be a lot of talk and investigation that goes on after that."