The Atletico Madrid defender lasted just 28 minutes of the encounter in Vienna before he was replaced by Thiago Silva with an apparent hamstring problem.
However, Dunga does not expect Miranda to be sidelined for an extended period of time.
"Miranda had an injury during the game and had to be replaced," he said. "The severity of the injury we will learn on Wednesday after further tests.
"Apparently there seems to be nothing serious."
Dunga also reiterated that he defends his decision to hand the captaincy to Barcelona forward Neymar in place of PSG centre-back Silva, who was reportedly unhappy at losing the role.
Silva did receive the armband in the closing stages when Neymar was substituted and Dunga wants more than just one leader in his side.
"The most important thing is not who is the captain, but who takes the lead," he added. "Yesterday I talked and I repeat here that we want leaders, we can't just have one inside the team."
Brazil's victory came thanks to Roberto Firmino's first international goal in the 83rd minute after Aleksandar Dragovic's penalty cancelled David Luiz's opener.
It was the South American nation's sixth win in succession since Dunga returned to the head coach role to replace Luiz Felipe Scolari following Brazil's disappointing home World Cup.
And Dunga believes the team are responding to his methods.
"The results show the work which has been done so far," he continued.
"All those teams we have beaten, Colombia, Ecuador and Argentina, have only lost to Brazil.
"The most important thing is that the players to understand our way of working."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.