"He won't go," Kubiak said on Friday. "He'll be out, but he ran very well today. He has made a lot of progress this week, so we're very close to having Andre back on the field, so that's exciting."
Johnson suffered the injury during Week 13's 17-10 victory over the Falcons. Earlier this season, Johnson missed six games with a right hamstring injury.
The five-time Pro-Bowl receiver has 31 receptions for 471 yards and two touchdowns in six games this season.
Houston has also ruled out starting guard Mike Brisial and cornerback Sherrick McManis for Sunday's game against Carolina.
The AFC South-leading Texans sit at 10-3 and have won a franchise-best seven straight games.