The 24-year-old was due to travel back to his homeland along with clubmate Philippe Coutinho to take on Uruguay and Paraguay in World Cup qualifiers, but has had to withdraw from the squad.
Initial reports suggested that Firmino's problem was bruising, but instead it has since emerged that it is another hamstring problem - the 16th that the Reds have suffered since Jürgen Klopp's appointment six months ago.
The news will be a frustrating blow to the German boss, whose tenure has coincided with the forward's best form in a red shirt, with Firmino scoring eight goals and recording four assists in 16 games in all competitions in 2016 alone.
Whilst there is not yet any indication of how long the Brazilian is set to spend on the sidelines, he will be assessed over the international break to determine the extent of the problem.
Reds without in-form forward for at least one match
Firmino was withdrawn after 85 minutes of the Reds' 1-1 UEFA Europa League last-16 second-leg draw with Manchester United on Thursday, albeit in a decision that seemed purely tactical as opposed to being motivated by any injury.
Benfica striker Jonas will replace him in the Seleção squad, the Brazilian FA have confirmed. Firmino originally missed out on the initial squad selection, until an injury to Kaka of Orlando City SC.
For Liverpool's trip to the south coast, Klopp could opt to field Coutinho alongside former Saints skipper Adam Lallana, with Divock Origi having been tipped for a start, alongside or in place of first-choice striker Daniel Sturridge.
The fixture against Ronald Koeman's men is their final fixture before the international break, which gives them a welcome two-week rest with tough games against Borussia Dortmund in the quarters of the Europa League and league meetings with Tottenham Hotspur and Everton, in the Merseyside Derby, to come next month.