Woods revealed to Cyclingnews that he was suffering with bronchitis, while Martin was similarly absent from the final roster issued by the team on Tuesday.
The reason given in both cases was "late developing health issues".
Woods indicated he's still on track for his first major objective of the season, the Ardennes Classics, where Martin, a former Liège-Bastogne-Liège winner is expected to co-lead later in April.
Martin kicked off his season at the Tour des Alpes Maritimes et du Var last week, where Woods won a stage and finished second overall. He is expected to join forces with Chris Froome at the Tour de France in the summer.
Michael Woods out of Tirreno-Adriatico with illness but determined to feature in Ardennes
Dan Martin: There are no egos at Israel Start-Up Nation - we're still underdogs
Dan Martin: What Chris Froome brings to the team is really underestimated
Dan Martin: I've proved, mainly to myself, that I can contest a Grand Tour
The duo's absence leaves Israel Start-Up Nation weakened for Tirreno-Adriatico, which starts on Wednesday and finishes next Tuesday. They will no longer be able to target the overall classification and are instead eyeing sprint opportunities on the flatter stages through Hugo Hofstetter and Davide Cimolai.
“We have excellent sprinters, with the whole team committed to lead them in the three sprint stages,” said team directeur sportif Nicki Sørensen.
"Add to that the opportunity for breakaways in other stages – and you’ve just got to bring ambitions, smarts, and aggressiveness to the highest level. This is the way we reach success here."
Breakaway specialist Alessandro De Marchi will lead the search for successful escapes, while Guy Niv will look to do the same on the hillier stages. Guillaume Boivin, Jenthe Biermans, and Mads Würtz Schmidt round out the seven-man squad.
"I suffered last year with the lockdown – that was hard on me mentally. I could not get it going. But now I feel that I am starting anew," said Cimolai.
"Hopefully, we can fight to win in the sprints and use this as the perfect preparation for Milan-San Remo."
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Try your first month for just £1 / $1 / €1
Thank you for signing up to Cycling News. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.