Clarke was ruled out of the rest of Australia's one-day international series with South Africa after re-aggravating the problematic left hamstring in the first match in Perth on Friday.
Clarke had scans on Saturday but needed to see specialists for a further prognosis.
Marsh said Clarke had been given a positive assessment initially.
"I'll back Michael Clarke in there (for the first Test)," Marsh told host broadcaster Channel Nine during coverage of the second ODI against South Africa on Sunday.
"I've never seen a happier doctor ... He looked really happy with what happened."
Australia play the first Test against India in Brisbane from Dec. 4 before further matches in Adelaide, Melbourne and Sydney.
Image: Michael Clarke
Photograph: Scott Barbour/Getty Images