The 72-year-old, who played for Arsenal in the 1960s and 70s, has cancelled forthcoming work and charity commitments including those for the Willow Foundation that he founded with his wife Megs.
The pundit, who retired from playing in 1974 but took up a coaching role with Arsenal for several years, was at Wembley for Saturday's FA Cup semi-final between the Gunners and Wigan Athletic. He is planning to return to public life as soon as possible, he said.
Wilson, the BBC and ITV television presenter, said: "I am very confident that the treatment I am receiving will prove successful and kindly ask that my privacy is respected at this time."
His son, BBC Radio 4 presenter John Wilson, said: "Knowing how strong my dad is, I have every faith he will be back to match fitness very soon indeed."
Wilson's daughter, Anne, died in 1998 aged 31 after succumbing to a rare form of cancer.
Her widower, 44-year-old Mitchell Carey, died in 2010 from food poisoning.
A Prostate Cancer UK spokesman said: "We wish Bob Wilson our best wishes in his fight against cancer.