Martinez reportedly suffered a heart attack during a dialysis session. Tuesday also marked his 66th birthday.
"This is just oh, so terribly sad," Martinez's wife, Olivia, told the New York Daily News. "He had so much to offer so many people."
Martinez was known as one of the most successful coaches in California community college history at College of San Mateo. Complications from diabetes led to serious health issues late in Martinez's life and he had been in need of a kidney transplant.
Last June, Brady told SI.com's Peter King that Martinez's influence over his career was "at the top of the list. Second to none."
Said Brady: "There is no one who knows more about throwing the football than (Martinez). And no one has meant more to me when it comes to throwing the football than Tom."
Olivia Martinez also told the Daily News, "We were convinced the dialysis was slowly killing him. UCLA (Medical Center) just couldn't be bothered to take someone at such high risk."
Martinez was rejected for a kidney transplant by the medical center.