Nassar, 59, was given a prison term of up to 175 years for abusing athletes.
After the incident on Sunday, he is allegedly in a hospital and in stable condition.
A prison union spokesman told NBC that the victim had a collapsed lung as a result of being stabbed six times in the chest, twice in the back, and twice in the neck.
Nobody on the staff or any other prisoners was hurt in the incident.
While affiliated with the USA Gymnastics program and Michigan State University, where he ran a clinic, Nassar admitted to sexually assaulting athletes.
The former doctor admitted to having child pornography in his hands. He is currently serving time at a federal prison in Florida.
At USA Gymnastics and Michigan State University, Nassar has been accused of sexually abusing more than 330 women and girls.
Olympic gold medalists McKayla Maroney, Aly Raisman, and Simone Biles have all spoken up in court about enduring Nassar’s torture.
Some of the young athletes claimed they had told adults, such as coaches and physicians, about the abuse but had been ignored.
An investigation into the FBI’s handling of the scandal, published in 2021, found the agency made a series of missteps, including delays and cover-ups, which allowed Nassar’s abuse to continue for several more months after the case was first opened.
The agency’s own watchdog found the FBI disregarded allegations about Nassar and made early errors in its investigation.
Several women who were sexually assaulted by Nassar – including Raisman, Biles and Maroney – have sued the FBI for $1bn (£783m) for mishandling credible complaints of sexual assault.
USA Gymnastics has agreed to pay $380m to Nassar’s victims, while Michigan State reached a $500m settlement with survivors.
An investigation into the FBI’s handling of the scandal, published in 2021, found the agency made a series of missteps, including delays and cover-ups, which allowed Nassar’s abuse to continue for several more months after the case was first opened.
The FBI committed a number of errors, including delays and cover-ups, which allowed Nassar’s abuse to continue for several more months after the case was first started, according to a 2021 probe into the bureau’s handling of the issue.
The FBI was found to have ignored the claims against Nassar and to have made early investigational mistakes by the agency’s own watchdog.
Several Nassar victims, including Raisman, Biles, and Maroney, have filed a $1 billion (£783 million) lawsuit against the FBI for improper handling of legitimate sexual assault claims.
In contrast to Michigan State, which struck a $500 million settlement with survivors, USA Gymnastics has agreed to pay $380 million to Nassar’s victims.
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