Rice, who started out as a player in the north London club's youth team, made 397 appearances for Arsenal over a 14-year period, winning the double in 1971 and leading the side to FA Cup glory against Manchester United in 1979.
Having finished his playing career at Watford, he worked under current manager Arsene Wenger from 1996 until his retirement in May 2012.
An Arsenal spokesman said: "We can sadly confirm Pat Rice is in hospital receiving treatment for cancer.
"Everyone at Arsenal Football Club sends him our best wishes. Our thoughts are with Pat and his family."
On the occasion of Rice's retirement last year, Wenger said: "Arsenal were privileged to have him as a captain, as a player, as a coach.
"Personally I'm very grateful for his contribution during my period here. He has been a constant and loyal supporter.
"Nobody is more of a fighter than Pat Rice."