Hammond, 47, was filming for The Grand Tour in Switzerland when the car he was in crashed and burst into flames, just moments after he managed to escape it.
His wife Mindy said she is "incredibly grateful" he managed to come out the other side without any major injury, apart from a broken knee.
Writing in the Sunday Express, she told how she found out from Hammond that he had been involved in the crash and the impact it had on their two daughters, Izzy, 16, and Willow, 13.
Calling her husband a "silly, silly boy", she said: "None of us in our little family dare consider what the outcome would have been if Richard hadn't scrambled his way out of that car last weekend.
"We're just incredibly grateful he got out and escaped with cuts, bruises and a broken knee.
"Before they loaded him on to the stretcher he called me, anxious to let me know he'd 'had a bit of a shunt' but was okay. James (May) spoke to me moments later and gave me a little more information."
She said Hammond was "downplaying what had happened" due to the shock of getting out of the car seconds before it burst into flames.
Mrs Hammond said she started to "feel peculiar" upon hearing the news as she was shopping with her eldest daughter.
After reassuring each other that Hammond would be fine, she added: "But in the back of my mind - and Izzy's too - were the memories of his last accident.
"I'm not a panicker, but I almost went to pieces this time.
"I didn't rant or get hysterical but my brain needed to keep itself occupied with something - anything - as long as it wasn't the reality of Richard's situation."
She wrote of her concerns that memories of Hammond's life-threatening crash in 2006 would resurface, but she added Willow was too young to have "vivid" recollections on that incident.
She said she is looking forward to having Hammond return home to begin several months of rehabilitation, and has praised a "guardian angel" for keeping him safe again.
"The girls have borne it well; we will go forward with a sense of humour and positivity; with enormous gratitude to that busy guardian angel who stepped in once more," she said.
"Most of us are fortunate to escape looking death in the face. Richard has done it twice - and that's two times too many."
Hammond's most recent incident - which left his Grand Tour co-star Jeremy Clarkson fearing he had been killed - came 11 years after he suffered life-threatening head injuries following a high-speed crash as he filmed for BBC's Top Gear in 2006.
The presenter was in a coma for two weeks following the 288mph accident, but made a full recovery.