Assistant coach Walter Samuel told a press conference that the Inter Miami superstar was "day-by-day" following an injury to his right adductor muscle.
"Leo had a problem in the last game, he won't be there for this game," Samuel said.
"We are going to go day-by-day waiting for its evolution."
Samuel, meanwhile, played down the impact of Messi's absence on the rest of the team.
"The team has always proven to be up to the task before when he wasn't there," said Samuel, hinting that veteran Angel Di Maria may start in place of Messi.
Argentina have already booked their place in the quarter-finals after wins against Canada and Chile in their opening two matches.
A draw in Saturday's game against Peru at the Hard Rock Stadium in Miami will guarantee Argentina qualify for the last eight as group winners.
Argentina is expected to rest several first-choice players against Peru, although Samuel insisted on Friday the world champions would seek a win.
"Peru has top players; we are taking this game with the utmost seriousness," said Samuel, who will be in charge on the bench with coach Lionel Scaloni serving a one-game suspension.
Scaloni and Argentina were sanctioned after the team were late to emerge for the second half in their games against Chile and Canada.
Samuel said Scaloni was "a little bitter" about the suspension.
"We consider ourselves a correct coaching staff and in all these years we've never had these kind of sanctions," Samuel said.
