The 64-year-old, who was connected to Arsenal as a player and then a coach for a total of 44 years, retired in May 2012.
An Arsenal spokesman added: 'Our thoughts are with Pat and his family. Everyone at Arsenal sends him our best wishes.'
Rice played over 500 times for the Gunners and Watford and also won 49 caps for Northern Ireland. Steve Bould took over from him as assistant last year.
After his retirement, he was awarded the MBE in the 2013 New Year's Honours list for his services to sport.
On his friend's retirement, Wenger said: 'Pat is a true Arsenal legend and has committed almost his whole life to Arsenal Football Club, which shows huge loyalty and devotion.
'I will always be indebted to him for his expert insight.'
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