Djokovic aggravated a right knee problem during his five-set win over Francisco Cerundolo, which was reported less than 24 hours later on Tuesday to be a torn medial meniscus.
Roland Garros organisers said: "Due to a torn medial meniscus in his right knee (discovered during an MRI scan performed today), Novak Djokovic, who was supposed to play Casper Ruud in the quarter-finals tomorrow, has been forced to withdraw from the Roland-Garros tournament."
The withdrawal means that Australian star Alex de Minaur would play Norwegian seventh seed Ruud in Friday's semi-finals should he beat Alexander Zverev in his quarter-final on Wednesday.
Ruud, the two-time finalist, gets a bye through to the last-four in Djokovic's absence.
Australian Open champion Sinner, just 22, will become the first Italian world No.1 when the new rankings are unveiled next week.
After beating Grigor Dimitrov 6-2 6-4 7-6 (7-3) to reach the semi-finals on Tuesday, Sinner had the news of his elevation to world No.1 broken to him on court by former French star Fabrice Santoro amid a standing ovation on Court Philippe Chatrier.
"What can I say? First of all, it's every player's dream to be number one in the world. In the other way, it's disappointing for everyone that Novak is out and I wish him a speedy recovery," said Sinner.
Djokovic reported on Monday that his knee problem had been bothering him for a couple of weeks before he arrived at Roland Garros — something he kept to himself until after the win against Cerundolo.
"I don't know what will happen tomorrow — or after tomorrow, if I'll be able to step out on the court and play," the 37-year-old had said. "You know, I hope so. Let's see what happens."
His withdrawal means Djokovic is still without a tournament win in 2024 and his hopes of finally going past the record of 24 grand slam triumphs he currently shares with Margaret Court will have to be put on hold.
But the injury could well mean he misses out on Wimbledon where he was expected to shoot for an eighth title.
In his remarkable comeback win over Cerundolo -- a record 370th victory in grand slam singles -- Djokovic, who slipped and tweaked his knee in the second set, had been left unhappy about the slippery conditions, and complained afterwards that the court should have been cared for better to help players' traction.
