Miller suffered the injury in the second quarter of the Bears preseason game Thursday against the Jacksonville Jaguars.
Miller, 29, was limited to only four games in 2011 and missed all of '12 and '13 with injuries before signing with the Bears in December. He is not to be confused with Seahawks tight end Zach Miller, who made the Pro Bowl with the Raiders in 2010.
Miller recorded six catches for 68 yards and two touchdowns in Chicago's preseason opener against Philadelphia.
“You guys saw him out at practice,” coach Marc Trestman said to reporters. “He had an excellent camp. Things transitioned from the practice field to the games over the last couple weeks. That was clear, and we were certainly excited about what we saw.”
A sixth-round draft pick out of Division II Nebraska-Omaha in 2009, Miller caught 45 passes for 470 yards and four touchdowns over his first three seasons.
The Bears' next preseason game is next Friday at Seattle.
- Chris Johnson