"I'm concerned with him going down with it, but we don't think that it's anything serious," Bears coach Lovie Smith said. "He'll be out, I would assume, for a while.
"We'll evaluate here a little bit later on in the day. He actually finished a drill so we think he'll be OK."
The Bears could bring in Gabe Lindstrom a former Toledo punter who they were considering early in camp.
Maynard is a valuable part of the defense. He netted a career high 38.7 yards per punt with just five touchbacks.
As the only punter in camp, the team tried to limit the numbers of punts Maynard had in practice. The Bears will add another punter to the roster.
Maynard wasn't the only sidelined Bear. Reserve safety Cameron Worrell was sidelined with a pulled hamstring and is out indefinitely.
Another concern was cornerback Jerry Azumah.
The Bears gave him off a second straight practice on Saturday. He had sat out Friday night's drills, as well.
Smith called it merely some rest.
Azumah last year missed much of training camp after suffering a stinger. It was later determined he needed neck surgery to correct a disc problem and he missed the first four regular-season games.
BUY A PROGRAM: The absence of Brad Maynard led to a humorous situation at practice. A fan began heckling the Bears' punter Saturday as he struggled to get the ball out of the end zone during special teams drills.
"C'mon, let's start getting it out there,'' the fan yelled as the ball went 20 or 30 yards.
"C'mon Maynard, kick that ball,'' he yelled a while later. The punter wasn't Maynard at all, though, but place-kicker Doug Brien who never punts.
The Bears immediately put Leon Joe to work with special teams Saturday.
Their second fourth-round draft pick in 2004 from Maryland was cut and claimed by the Cardinals, then cut by Arizona last month. The Bears re-signed him Friday night.
"It really feels good, it feels like a homecoming because everyone knows my name," Joe said. "They're looking for me to do good things."
Joe was unimpressive his first time around, but general manager Jerry Angelo had called him the one player he most wished he had back who he had to cut.
The Bears waived Joe Sept. 15 last year. The 6-foot-1, 235-pounder was claimed by Arizona and played four games for the Cardinals while being inactive 11 games.
"Obviously they decided I wasn't ready to play here," Joe said. "This year, I have a different mindset and a different attitude. I was surprised when they let me go."
Joe was arrested last month on a charge of carrying a pistol without a license in Washington D.C. and still must face charges.