The Rockets were short-handed, too, with rookie forward Carl Landry sidelined with a bruised right knee.
West, the Hornets' second-leading scorer and rebounder, rolled his ankle in the second half of New Orleans' 100-88 victory over the New York Knicks on Monday night. He remained in the game, but then missed the Hornets' victories over Atlanta and New Jersey.
Hornets coach Byron Scott said the 6-foot-9 West should be ready to play against San Antonio on Wednesday.
"By Wednesday, both those guys will be pretty healthy and they'll be ready to go," Scott said.
The 6-9 Landry, a key player in Houston's current 17-game winning streak, hurt his knee in Wednesday's 117-99 win over Indiana. He played in Thursday's 113-98 win in Dallas, scoring 17 points with two rebounds.
Landry has averaged 10 points and five rebounds during the Rockets' franchise-record victory streak.
"Hopefully, I can get back on the court some time soon," Landry said. "I'm walking fine."
The Rockets signed Mike Harris to a 10-day contract to replace Landry. Harris signed with the Rockets as a free agent last July and averaged five points and six rebounds in Houston's first two preseason games this season. He was released on Oct. 22 and has been playing in China.