The superstar forward was brought off during the second half of Barca's 1-1 LaLiga draw against Atletico Madrid at Camp Nou on Wednesday.
Barca later confirmed that the 29-year-old is set to miss around three weeks of action with a groin strain, with Messi having suffered a similar injury during the last international break with Argentina.
And Bauza has hinted at an air of hypocrisy from Barca, claiming the Catalan club are guilty of overusing their star player.
"Barca have sent us messages to ask us to look after Messi, but they don't seem to take care of him much themselves," he told Fox Sports.
"It seems really strange that they make him play every game with the problems that he has."
Bauza says Argentina are now waiting to see the results of Barca's medical tests to assess the full extent of the injury, but he does not expect Messi to play in World Cup qualifiers against Peru and Paraguay next month.
He added to ESPN Radio: "What we got was an official notice from Barcelona that Lionel has a rupture in his right adductor, out for three weeks. It seems odd to us because three weeks is not enough to recover from a ruptured adductor.
"We still haven't been able to talk with him, but we want to know what the severity is.
"Apparently he had a test and we're waiting for the results to be sent to the national team doctor, and then we'll have a clearer view.
"For me, Messi will not be able to play in the knockout games. We hope it's not serious and that in three weeks he'll be playing again. We're already thinking about playing the games without him.
"Barcelona don't make things difficult for us. They sent an official notice and until now it's the only thing we have. The national team doctor is waiting for the pictures to know what the official grade of the injury is."
Bauza is now pondering his options without Messi.
"Things won't change much tactically without him. We have a lot of options, we'll look at them when the players are all together," he said.
"[Paulo] Dybala could play on the right, we also have [Angel] Di Maria, Augusto Fernandez, [Erik] Lamela or [Nicolas] Gaitan. We have to wait until they come to see who is best."
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