A firefighter who was allowed to graduate the Fire Academy despite failing physical tests has already gone out on medical leave — just 10 days into the job, The Post has learned.

Probationary firefighter Choeurlyne Doirin-Holder injured herself Monday while conducting a routine check of equipment at Queens’ Engine 308 in South Richmond Hill. Getting off the truck, Doirin-Holder missed a step and landed on her left foot, suffering a fracture, sources said.

It was her second shift after a transfer from Engine 301. In training for a hazmat assignment, officers found her struggling to perform the required tasks.

Firefighters called the tripping incident embarrassing — and alarming.

“If you’re going to get hurt in the firehouse checking a rig, what would happen at a fire?” an insider asked.

On Nov. 6, Doirin-Holder celebrated her FDNY graduation as one of four new female Bravest, bringing the number of women to 49 — an all-time high in the FDNY’s 150-year history.

But Doirin-Holder’s competence was questioned by sources familiar with her training. They said academy instructors let her pass the Functional Skills Test, a rigorous obstacle course of job-related tasks, even though she had failed to complete it in the required 17 minutes and 50 seconds or under.

In addition, when she failed to finish a 1.5-mile run in 12 minutes or less — even after the course was shortened — she was allowed to demonstrate aerobic capacity on a StairMaster machine under watered-down requirements enacted by FDNY Commissioner Daniel Nigro.

Doirin-Holder, who turns 40 this month, is one of 282 “priority hires” passed over in 1999 and 2000. Federal Judge Nicholas Garaufis ordered they must get preference as victims of past discrimination against minorities.

It was Doirin-Holder’s third attempt to pass the academy. She failed midway through an academy class in 2013 and returned to her former job as an EMT. Two other female priority hires in that class did well.

Doirin-Holder started another class in early 2014 but dropped out because of an injury. The FDNY then gave her a desk job and kept her on the payroll at top firefighter salary, $76,488. She made $81,376 with overtime in 2014 and entered her third class this summer.

Since she was injured on duty, she is eligible for a disability pension that would pay three-quarters of her annual salary, tax-free, if deemed unfit to return.

In an online FDNY forum, firefighters fumed at the preferential treatment.

“If you can’t meet the standards, you are a danger to yourself, the public and most importantly everyone operating on the fire ground who is doing their job,” one wrote.

The FDNY said it won’t discuss personnel or medical matters.