"Don't know yet, he's just kind of day to day," coach Mike Woodson said. "He's getting treatment and we'll see where he is come Monday."
Anthony has yet to undergo an X-ray or MRI to determine the extent of his injury.
A source close to Anthony says that he wants badly to play against the Rockets but, as of Sunday evening, his status was uncertain due to lingering effects of the injury.
Anthony, according to a team source, is expected to test the injury some time prior to tip-off on Monday, most likely during the team's shootaround on Monday morning.
"It definitely caught me off guard," Copeland said of his first career start, "but it's such a blessing for the opportunity altogether. Carmelo's a special guy, he's a special player. I just want to go out there and play my game and do the best I can."
Saturday was Anthony's third missed game of the season.
He missed two games earlier this month with a laceration on his left middle finger that required five stitches.
The Knicks (17-5) went 1-1 with Anthony out, beating Miami by 20 points and losing to Chicago, both on the road.
"When one guy goes down, another guy steps up. It has to be continuous throughout the entire year," Tyson Chandler said after the Knicks' win over Los Angeles on Thursday.
Anthony left Thursday's game midway through the third quarter after a collision with Dwight Howard on a drive to the Lakers' basket.
Anthony hit the floor hard and landed awkwardly on his left ankle, and his lower left leg folded under his back as he hit the court.
After a few moments on the floor, Anthony stood up and gingerly walked to the free throw line. He hit 1-of-2 free throws and was subbed out of the game at the next horn for Steve Novak.
"It was a hard foul. I couldn't catch my fall," Anthony said after the Knicks' 116-107 win against the Lakers. "It was an awkward fall. Right now, I'm sore."
General manager Glen Grunwald said after the game that he did not believe the injury was serious. The team says Anthony did not undergo X-rays to further examine the injury.
Anthony was in the midst of a fantastic offensive performance before he left with 6:33 remaining in the third quarter.
He scored 22 points in the first quarter -- two shy of the franchise record by Willis Reed and Allan Houston -- and had 30 points on 10-of-15 shooting at the time of his exit. He played just 23 minutes.
Ian Begley is a regular contributor to ESPNNewYork.com. Information from ESPNNewYork.com contributor Jared Zwerling was used in this report.