"Most upsettingly" the couple say the burglars made off with her engagement ring.
They broke in after they and the friends with whom they were sharing the villa had gone to bed.
A spokesman for Button said: "Jenson, Jessica and friends were on holiday in a rented villa in St Tropez when on Monday evening two men broke into the property while they all slept.
"(They) 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 so 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."
Button, his wife and three friends apparently left the villa immediately after discovering the robbery and informing police.
According to The Sun newspaper, the intruders made off with £300,000 worth of goods including the five-carat ring.
The ring, a three-stoned large teardrop design diamond set in a diamond-encrusted platinum band, is said to be worth around £250,000.
Button and Michibata, who grew up in Japan, married in December after meeting in 2008.
He dedicated his world championship win to her the following year.
The McLaren driver, 35, has been tipped as a possible future co-presenter on Top Gear.