The South Africa-born Englishman has been battling the injury all year after originally hurting the shoulder last August.
"While ... rehabilitation continues to help the persistent tendinitis in Justin's right shoulder, scheduling four straight weeks of competition was aggressive to start the season. Therefore, Justin must withdraw from this week's Honda Classic," , the world number six's camp said.
Rose played in the last two US PGA Tour events, tying for 45th in the Northern Trust Open before losing to Ernie Els in the second round of the World Golf Championships-Accenture Match Play Championship.
He still is hopeful for next week's World Golf Championships-Cadillac Championship at Doral, where he won two years ago.
Six of the world's top eight players, including world number one Tiger Woods, are scheduled to compete in the Honda Classic, which begins on Thursday at Palm Beach Gardens, Florida.
The field also includes Australian world number two Adam Scott, Swede Henrik Stenson (3), Phil Mickelson (5), number Zach Johnson (7) and Northern Irishman Rory McIlroy.