Savea's wife, Fatima, posted the news on her Instagram account saying Savea was "safe and sound."
"Count your blessings everyday (sic) guys," she wrote in an Instagram story.
"Tonight Julian fell asleep behind the wheels of his car and flipped his car. Thankfully he is safe and sound in bed with me now after being dropped home by the ambulance because silly me had her phone on silent and missed all the calls and texts.
"If you know Julian you'll know he falls asleep anywhere at any minute (A problem he's always had) so I'm thankful to god for bringing him home safely to Jude and I and for protecting him tonight.
"I can't stress to you enough how important it is not to drive while you're tired Julian was lucky tonight."
The incident happened after the 28-year-old former All Black's club side Toulon's win over Perpignan in the French Top 14 competition.