Joseph, who went to the Pro Bowl last season, sustained the injury in the second quarter of the Texans' 37-13 loss to the Broncos.
The eight-year veteran has been with Houston since being acquired as a free agent in 2011. He has 55 tackles this season, one tackle for loss, three interceptions and 16 passes defensed.
"We lost J. Jo during the game, which obviously hurt us," Phillips said Sunday. "He's our best corner. Any kind of matchup thing we lost."
Running back Dennis Johnson is questionable with a hip injury, Phillips said. If he can't play, the Texans will start Jonathan Grimes, who was in training camp with the team last season after going undrafted. Grimes would be the fifth running back to get a significant load in a game. Starter Arian Foster and backup Ben Tate are both on injured reserve.
Houston will bring a franchise record 13-game losing streak to Nashville this weekend.