The 33-year-old opening batsman, who retired from international cricket this year, will return home to undergo surgery.
Surrey have signed Smith's former South Africa team mate Hashim Amla for the next month.
"Whilst it is obviously a huge blow for Graeme to be heading home, especially after his recent match winning hundred, and with the impact he was having in the dressing room, we are very fortunate to be able to welcome back Hashim Amla for the next month," Surrey director of cricket Alec Stewart told the cliub's website.
Smith played 117 tests, 108 as captain, and scored over 9,000 runs.
(Reporting by Ed Osmond; editing by Justin Palmer)
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