Starc is suffering bone spurs in an ankle but has been retained in Australia's 15-man squad for their tour of Bangladesh, even as fellow left-armer Mitchell Johnson and Josh Hazlewood are rested.
"My understanding of Starc is that he can keep going until it actually gets a hell of a lot worse, and then he will have to have an operation," selectors chairman Marsh said in Adelaide.
"Rest won't help him.
"He has got spurs in his ankle and there is a bit of bone that has broken off and floating and every now and then it gets into a position where it is just chronically painful.
"Eventually it is going to have to be removed but it will take another three or four months after the operation for him to be able to play again.
"We have got some pretty important cricket coming including the T20 World Cup and we would like to see Starc lead the attack for that... but if he can't, he can't. But at the moment the plan is for him to keep going."
Named the best player at the World Cup in Australia and New Zealand earlier this year, Starc has been troubled by his ankle for months and needed pain-killing injections to get him through the Ashes series, which Australia lost 3-2.
He missed the fourth one-day international against England but after having a cortisone injection, returned for the decisive fifth and final match in Manchester on Sunday which the tourists won to seal the series 3-2.
After five months on the road, Starc will return home to Australia for 10 days' rest before packing his bags again to head to the subcontinent for the two-test tour of Bangladesh.
"To be honest, it's nice to be going home for a little bit [to have] a few days in my own bed and see the family," Starc said in Manchester.
