Tony and his wife, Linda, have four children, Michael, Dominic, Nicholas and Gabriella. Michael and Dominic both play baseball, hockey and practice karate. He served as guest radio host on KNBR 68 during the afternoon of August 24, filling in for the vacationing Gary Radnich, with co-hosts Bernie Nicholls and Dan Rusanowsky. Last summer, he went to Disneyland with his family and went fishing with his children. Tony's sister Cammi served as captain of the gold-medal winning U.S. Women's National Hockey team at the 1998 Olympic Games in Nagano, Japan and was named radio color commentator for the Los Angeles Kings this season. His brother Don is general manager/coach of the Columbus Chill (ECHL). Tony became the first Sharks player to capture a major postseason award by the NHL when he was awarded the 1997 Bill Masterton Trophy representing "perseverance, sportsmanship and dedication to hockey." An avid baseball fan, he grew up watching the White Sox and followed the Angels while in Southern California. He also likes bass fishing, having landed a 10-pounder once.

The 1996-97 Masterson Trophy winner for preserverance, sportsmanship, and dedication to hockey, Granato successfully returned to play hockey for San Jose in the same year, just 6 months after undergoing brain surgery to remove a blood clot. In just his second game back with the Sharks, he registered his seventh career hat trick versus Los Angeles. Capable of playing either wing, Tony was a member of the NHL All-Rookie team in 1988-89. He has become a leader and a role model with his gritty and relentless style.