"Wade Phillips has completed the surgery on his kidney and gallbladder," the statement read. "He is in stable condition. In order to respect his privacy, the family has requested there be no further information given at this time."
Phillips announced on Wednesday that he was going to take a medical leave from the team after undergoing a scheduled surgical procedure, but is expected to return to his duties later this season.
The AFC South champion Texans own the NFL's top-ranked defensive unit under Phillips, who was hired in January after being fired as head coach of the Dallas Cowboys last November.
In the interim, linebackers coach Reggie Herring will call the defense. Herring coached the linebackers with Dallas from 2008-10 under Phillips.