The injury took place in Friday's 15-8 win over the Boston Red Sox at Chase Field.
The catcher homered off Red Sox infielder Eduardo Nunez, who was on the mound late in the Diamondbacks victory.
The catcher ran hard out of the box when he hit the ball unsure if it was going over the fence, and once it was ruled a home run he pulled up, which is when the quad tightened.
"We thought it would make a lot of sense to make that move and give him a little blow, and get him back on his feet and get him 100 percent," D-backs manager Torey Lovullo said via the Diamondbacks official site. "So we thought a 10-day situation would be perfect."
With Avila on the injured list, the team recalled outfielder/infielder Tim Locastro from Triple-A Reno.
Avila is hitting .333 with two homers and five RBIs in six games.