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The 28-year-old took to Twitter to express his gratitude for his fans' well wishes.
"Just want to thank everyone for the messages and concerns about my accident," Savea wrote on the social media platform.
"I am just very grateful that no one else was involved and hurt and that I made it home safely to my wife and daughter."
The incident happened after the former All Black's club side Toulon beat Perpignan 26-16 in the French Top 14 competition.
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."
She also said alcohol was not involved in the crash.
"And before anyone makes any assumption, no alcohol was involved.
"Firstly, he's been sober 8 months (woohoo). Secondly, the police did a full test etc and lastly, who's dumb enough to drink and drive?"
Savea – who hasn't had the best start to his time in France – was able to end his try-scoring drought in the match, and made his first start in the midfield, alongside fellow former All Black Malakai Fekitoa.