Almiron was withdrawn after 64 minutes of the game at St. James' Park and the club have announced he will subsequently miss the final three games of the Premier League season.
Of greater importance is his participation in the South American showpiece which gets underway in Brazil in June.
Paraguay were drawn in Group B alongside Argentina, Colombia and Qatar and will be hoping the 25-year-old, who was sent-off on his last international appearance - a 4-2 defeat to Mexico last month - can recover in time.
A Newcastle statement read: "Miguel Almiron will miss the rest of the season after suffering a hamstring injury in Saturday's 3-1 win over Southampton.
"The 25-year-old was withdrawn in the 64th minute against the Saints and having been assessed by the club's medical staff, it has been confirmed that he will not be fit for the Magpies' final three matches of the campaign.
"The club have already been in communication with - and will continue to liaise with - the Paraguayan Football Association ahead of this summer's Copa America, which the player could still feature in depending on his recovery."
Newcastle splashed out a reported club-record fee of £21million to sign Almiron from Atlanta United in January and, although his performances have been warmly received, he is yet to register an assist or score a goal in 10 league appearances.
However, the Magpies have won five and drawn two of the games in which he's featured, failing to score just three times in their three defeats in that period.
They sit 13th, 10 points clear of the relegation zone and are mathematically safe with just three games left to play.