The marble tomb, bearing carvings depicting the 12 labours of Hercules, dates to 2 AD.
It was found by customs officials who were carrying out inventory checks at Geneva's tax-free warehouses, said Jean-Marc Renaud, who heads Switzerland's central customs services, confirming a Swiss television report.
According to Swiss television, Ankara is seeking restitution of the sarcophagus believed to have originated from the Greek-Roman archaeological site of Perge, about 22 kilometres from Antalya.
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Swiss customs are currently holding the object, and have brought the case to Geneva prosecutors which opened a probe last year.