The 21-year-old suffered a syndesmosis injury to his left ankle at training last week.
The Cats are not willing to put a timeline on Miers' return.
"Gryan is an important player for us, as he has shown over the past three years," Geelong's football manager Simon Lloyd said.
"We reviewed the scans and considered all possible options before determining that surgery was required.
"As we have seen with this type of injury, it is difficult to outline a return date, as everyone heals and rehabs differently.Â
"Gryan will undertake his rehabilitation diligently and professionally to get back on the field as soon as possible."
Miers has played 61 games for the Cats since debuting at the start of the 2019 season, kicking 59 goals.
Experienced ruck recruit Jonathon Ceglar, who moved from Hawthorn in the off-season, also had surgery for a knee issue but is expected to make a quick recovery.
Geelong, who suffered a painful defeat in last year's preliminary final against Melbourne, are due to open the 2022 season against Essendon at the MCG on March 19.
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