An employee set off an alarm but police arrived after the thieves had fled, police said in a statement.
"Despite my age, I struggled with one of them," 75-year-old Elie Chatila, who estimated his loss at several million francs, told the daily Tribune de Genève. "Look at this, they left a ring worth more than SFr500,000".
He described the shop as being in a "catastrophic state".
A police spokesman said that detectives were analysing finger prints and DNA found at the crime scene.
No clear link had been established to the "Pink Panthers", an international gang of jewels thieves who have carried out attacks on luxury stores in Paris, London and other European cities in recent years, police said.
Geneva is a popular summer destination for wealthy tourists from Gulf countries, who flock to the lakeside city to escape the heat and shop at luxury boutiques along the smart Rue du Rhône.