Greenard is expected to miss four to six weeks, according to Schefter.
He previously missed the Texans' victory over the Jacksonville Jaguars in Week 5 with an ankle injury.
Greenard, a 2020 third-round pick out of Florida, is third on the team in sacks with 1.5 this season after having eight sacks in 2021.
The Texans are also hopeful their offseason signing of defensive end Mario Addison can help. Addison, who missed the first four games with a thigh injury, had seven sacks last year for the Buffalo Bills.