Pitts sprained the medial collateral ligament in his right knee in the second quarter of Sunday's 34-31 victory against the Tennessee Titans.
Pitts is the only player to have started every game in Texans history, and with the surgery, his streak of 114 consecutive starts will end Sunday, when the Texans face the Jaguars.
"Obviously, he's going to miss some time. How much depends on [the surgery]," Texans coach Gary Kubiak said.
Pitts was hurt protecting quarterback Matt Schaub on a 21-yard completion to Joel Dreessen with 4:41 left in the quarter. He stayed on the ground for a few minutes before being helped to the sideline.
Former Texas standout Kasey Studdard, a third-year veteran who filled in Sunday after Pitts was injured, will take his spot in the lineup.
"Kasey plays the game on emotion and effort," Kubiak said. "He fits with the group. There was no fear there [after Pitts' injury during the game] as far as where we were going or how we were going to do. Our guys expected him to do his job, and he did. I'm excited to see him play. He's earned the right to play."
Information from The Associated Press was used in this report.