Scott Paterno said in a statement that the cancer was discovered during a follow-up visit for bronchial illness.
"He is currently undergoing treatment and his doctors are optimistic that he will make a full recovery," Scott Paterno said. "As everyone can appreciate, this is a deeply personal matter for my parents, and we simply ask that his privacy be respected as he proceeds with treatment."
The announcement came less than an hour after Penn State said the NCAA would examine how school officials handled the Sandusky scandal. The former Penn State defensive coordinator Sandusky is charged with sexually abusing eight boys over 15 years.
Paterno was accused of not doing enough to report and stop the abuse.
NCAA president Mark Emmert said in the letter to Penn State president Rod Erickson that the governing body for college sports will look at "Penn State's exercise of institutional control over its intercollegiate athletics programs."
The faculty at Penn State called for an independent investigation into how the university handled the child abuse accusations. There are indications the faculty may get its wish. No one affiliated with the university will be involved in the investigation.
Sandusky founded a charity called Second Mile to help disadvantaged youth. Pennsylvania's attorney general says Sandusky met the boys he is accused of raping and assaulting through the foundation. Now, Second Mile is trying to transfer its programs to other nonprofits.
Emails have been flooding the Penn State Alumni Association and Board of Trustees. Some alumni say they've stopped all donations to the university, while others won't resume until there is more action.
The association president said there is a unity of concern for the victims and their families.
"We're seeing this in everything, for the victims and their families, and they want Penn State and the Alumni Association to make things right. Our state needs us, our country needs us, our world needs us and we need to get Penn State back to where it was and better than where it was before," said Roger Williams of the Penn State Alumni Association.
See photos of Penn State students reacting to the firing of Joe Paterno.
The Associated Press contributed to this report.