Cavendish finished 30th in the ‘Hell of the North’ cobbled classic last year and was due to ride the gruelling race for only the third time.
The 30-time Tour de France stage winner will now take some rest before targeting more success at the Grand Boucle in July.
“Mark sustained an overuse injury of his right ankle while competing at the Tirreno-Adriatico race,” said Dimension Data’s team doctor Jarrad Van Zuydam.
“The injury was thought to be resolving but has unfortunately flared up again during training.
“Further investigation and treatment is necessary over the coming days to resolve the injury before Mark returns to racing.”
Cavendish will also miss Wednesday’s Paris-Roubaix warm-up race Sheldeprijs, which the Manxman has won three times.