This comes only five months after the former United skipper's 34-year-old wife, Feziwe, lost her fight against bowel cancer.
Radebe's planned visit to Leeds later this week has now been postponed until later in the year.
The 39-year-old South African was due at a dinner in his honour at Elland Road on Friday.
He was also scheduled to attend Leeds's home game against Swindon Town the following day.
United said the dinner had been re-arranged for Friday, May 15. A spokesman said the club sent its "sincere condolences" to Radebe and his family.