The Formula One racer, 35, and Jessica were staying with friends in St. Tropez when the incident occurred.
It is thought that the thieves pumped gas into their luxury villa through the air conditioning vents before breaking in and stealing around £300,000 worth of goods.
A spokesperson for that star said: “Jenson, Jessica and friends were on holiday in a rented villa.
“Two men broke into the property whilst they all slept and stole a number of items of jewellery including, most upsettingly, Jessica’s engagement ring.
“The police have indicated that this has become a growing problem in the region with perpetrators going as far as to gas their proposed victims through the air conditioning units before breaking in.
‘Whilst unharmed, everyone involved is unsurprisingly shaken by the events.”
According to reports, Jenson, Jessica and their three friends had no idea that the robbery was taking place – as the gas had knocked them all out cold.
A source told The Sun: “They weren’t disturbed at all because the effects of the gas gives the burglars free reign.
“It was the same for their three other friends – they were all completely out of it.
“The first they were aware was when they woke up groggy the next morning and realised the house had been turned upside down.”
Model Jessica, who grew up in Japan, married Jenson in December last year on the island of Maui.
The ceremony was an intimate one, with the couple tying the knot in front of just 40 close friends and family members.