"I'm extremely disappointed to be missing the start of the season," the 26-year-old said in a statement.
"I was looking forward to heading over and joining the Surrey family. I'll be doing everything I can to get myself fully fit and hopefully join the side later in the season."
Marsh has been in fine form since his recall to the Australian side for the third Ashes test, averaging more than 45 with the bat against England and South Africa.
A Cricket Australia spokesperson said Marsh is targeting a return for the start of the Australian summer, suggesting the player will miss the limited-overs tour of England in June.
He will also face a race against time for Australia's next away test campaign against Pakistan, which is expected to be held in September or October this year.
(Reporting by Hardik Vyas in Bengaluru; editing by Amlan Chakraborty)
