The 36-year-old has not played since January 23 at Sunderland and picked up a second hamstring injury of the season shortly afterwards.
Boss Steve Cotterill opted not to register the veteran frontman, who has scored once in 10 games for Town, as part of his 23-man EFL squad available for action, as No.2 Aaron Wilbraham cited the possibility of having to instead sign a free agent defender during an injury crisis.
And, while taking time out of the action, former Wolves man Clarke has had surgery on a blood clot to his back, and is now undergoing rehab.
“Leon picked up another hamstring injury in training a few weeks ago,” Wilbraham said. “He was outside on the grass joining in and another who was going to be back involved but he pulled up in training.
“He had a scan on a four to six week injury and he also had an operation that he needed on his back, it was a little blood gathering, nothing serious but it needed doing.”
Clarke was signed on a one-year deal by former boss Sam Ricketts in September but has managed just six starts for the club. He netted a dramatic late winner at AFC Wimbledon for Town’s first league win of the season.
Wilbraham said Clarke was on the verge of being re-included in Cotterill’s registered squad prior to his latest setback.
“It made sense for Leon and everybody else for him to have it while he was out injured,” Wilbraham added. “That’s where Clarkey’s at.
“But he was in earlier this week doing his rehab and that, it’s been unfortunate for him with a couple of hamstring injuries at bad times, just when it seemed he was getting somewhere it’s happened again.
“The gaffer was on the verge putting him back in and then it happened so there was no point filling in the last space with an injured player.”
Clarke is thought to be one of those unlikely to earn a new deal at Montgomery Waters Meadow in the summer.
The striker, who has had 18 clubs, is one of several first-team squad members out of contract.