The team said the Australian developed a chest infection after Volta ao Algarve where he finished 27th overall and over four minutes behind race winner Michal Kwiatkowski (Sky)
"Richie Porte developed an upper respiratory infection after Volta ao Algarve which forced him to miss the best part of a week's training," BMC Racing Team Chief Medical Officer Dr. Max Testa said.
"Given Tirreno-Adriatico was one of Richie's goal races this season, it did not make sense to line up when his preparation was far from ideal."
Porte had geared his run up the Tour de France with the stop at Tirreno which contained the right mix of mountain and time trial stages for a Grand Tour rider and one where he was expected to make his presence felt.
"Richie and the BMC Racing Team management and medical team agreed that it was in his best interests to miss Tirreno-Adriatico and adjust his race program, in order to recover properly," Testa said.
It was not revealed which race would replace Tirreno-Adriatico but the Volta a Catalunya on 19 March will be the next important WorldTour stage race.
The team said Damiano Caruso will assume team leadership at Tirreno while Australian Rohan Dennis will target the time trial stage.
"I'm looking forward to going back to Tirreno-Adriatico next week," Dennis said. "One main goal of the team will be to win the opening team time trial again, and we are motivated to do that.
"For me, the individual time trial will, of course, be another target and I hope to repeat my success from last year. In between the two, we will see what happens."