The fans of the legendary British rock veterans tried to force their way into the Monumental football stadium as about 10,000 concert-goers with tickets were waiting at security gates to be admitted, police said.
As officers tried to drive back the gate-crashers with water cannon, the fighting broke out.
The concert, which was the second and final show for the Rolling Stones in Buenos Aires as part of their Big Bang world tour, began 20 minutes late.
A total of 65,000 tickets were sold for Thursday night's show.
