Hayden, who had a good tour of India in 2001, said Gambhir formed a "potent" opening combination with Virender Sehwag and the left-hander's exclusion will be a welcome relief for the Australian bowlers.
"The fact that India has dropped Gautum Gambhir is a positive step for Australia," Hayden said about the diminutive left-hander, who struck a century for India A against Australia in a warm-up game on Saturday.
"He always rallied when playing Australia and that combination of Virender Sehwag and Gambhir was a very potent one ... Gambhir relishes the niggle and returning fire. It was a big surprise they left him out," he was quoted as saying by The Daily Telegraph.
Hayden, who turned out to be a nightmare for the Indian spinners during the 2001 series, came up with a list of dos and don'ts for the touring Australian contingent in order to achieve success on Indian soil.
He gave advise to the Australian batsmen on how to tackle the turning ball on Indian pitches.
"Going to India, there is always a big mention of their spinners. I don't think we should buy into that too much. It's a spinning ball, it's not like it is coming down on you at 165km/h," said Hayden, who made an incredible 549 runs at an average of 110 during the 2001 tour of India.