The European Tour event at Wentworth Golf Club starts Thursday. Spain's Miguel Angel Jimenez is the defending champion.
Rose, a 10-year tour veteran, has not played in a tournament since the PGA's Players Championship at Ponte Vedra Beach, Fla., this month.
He has been plagued by back problems throughout his career.
"This has been a tournament that I have always loved competing in and is the main reason we traveled back, so having to withdraw is very frustrating for me," Rose, who lives in England, told the BBC Wednesday. "It has been even more hectic this year traveling back with Leo (his son, born in February), where we have been taking him to meet all the extended family and friends."
Scotland's Richie Ramsay will enter the field in Rose's absence.