The 2013 Tour de France champion confirmed his non-attendance via Twitter on Monday morning, and the team later confirmed he was suffering with a chest infection.
"This is obviously frustrating after the good start that I've had to the season, but it's a minor setback," said Froome via a team statement. "I've been ill for a few days now and unfortunately I couldn't shake it off in time for the race.
"After speaking with the doctors we decided as a precaution that it would be best to take a few days off the bike to recover fully."
Froome is aiming to return to racing at the Volta a Catalunya, March 23-29.
Froome was due to lead Team Sky at the prestigious Italian stage race as part of his build-up towards this year's Tour de France. He would have started the race as one of the favourites for the overall victory having won Ruta del Sol against Alberto Contador (Tinkoff-Saxo) at the end of February.
Team Sky's revised line-up for Tirreno-Adriatico is Vasil Kiryienka, Leopold König, Mikel Nieve, Wout Poels, Salvatore Puccio, Ian Stannard, Elia Viviani and Kanstantsin Siutsou. No replacement for Froome has yet been announced, but it would seem likely that König or Nieve will take up leadership duties.
Tirreno-Adriatico runs from March 11-17 and includes a star-studded list of starters, even without the presence of Froome: Contador, Vincenzo Nibali (Astana), Nairo Quintana (Movistar) and Rogoberto Uran (Etixx-QuickStep) will all be vying for the win.
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