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Landa, who finished third last year and was among the race favourites, was trailing from the first climb of the 219km stage between Campi Bisenzio and Sestola.
His team-mates and fellow Spaniards David Lopez and Mikel Nieve tried to encourage the 26-year-old but he was trailing by over six minutes by the 50km mark, and finally gave up 15km later at the base of the second climb of the day.
Landa had made the Giro his main objective this season since joining Sky from the Astana team. He won the Tour of Trentin last month, one of the warm-up races for the Giro.
Despite failing to make his mark during the first week of the race he came back in Sunday's time-trial in Chianti and was eighth overall 1:18 behind leader Gianluca Brambilla of Italy.
Sky have a recent history of losing their leader at the Giro after Bradley Wiggins pulled out sick in 2013, and Richie Porte pulled out after in 2015 after a series of bad luck and a fall left him trailing badly in the overall standings.
