Messi initially picked up an issue on international duty earlier this month, but did not miss any club football and aggravated the problem in Wednesday's 1-1 draw with Atletico Madrid in the league.
Bauza has claimed that Messi's recent injury is down to Barcelona not resting the attacker, who is now expected to miss Argentina's World Cup qualifiers against Peru and Paraguay next month.
"Barca are always sending us messages that we must take care of Messi, but it is them who are not taking proper care of him," Bauza told Fox Sports.
"It is strange that they make him play in all their matches. We received the official report from Barcelona and to us it seemed strange because three weeks is not long enough to recover from a torn adductor muscle.
"We have not been able to speak to him yet but we want to know how serious the injury is - Barcelona have made it more complicated for us. Apparently studies have been done and we are waiting the results of those, which will be sent to our national team doctors. That way we will have a more definitive answer."
Messi initially retired from international duty after representing Argentina in the Copa America earlier this summer, before reversing the decision.