The Houston Chronicle reported Phillips was expected to miss Sunday's home game against Carolina and a Dec. 22 game in Indianapolis.
Phillips, who heads the NFL's top-ranked defense, said he hopes he'll return for the season's final game Jan. 1, a home game against Tennessee.
Reggie Herring, the linebackers coach who worked under Phillips in that job in Dallas from 2008-10, will call plays.
"It's going to be a little different as far as with Reggie making the calls now instead of Coach Phillips making the calls, but like I said, they've worked together for so long where I feel like both of them think alike in the same situations," inside linebacker DeMeco Ryans said. "I feel like there will be similar calls in similar situations."
"It's all Wade's system still, all his same calls," said outside linebacker Connor Barwin. "He's already got the game plan in. It's just going to be a different person giving the hand signals or talking to DeMeco in the headset."