The 83-year-old cricketer-turned-commentator ended up with chest and shoulder injuries, besides a broken sternum, when his 1963 Sunbeam Alpine "mounted a nature strip and hit a small brick wall".
"No one else was injured, and I was more worried about the car than myself," Benaud said in a statement.
He is expected to be hospitalised for two weeks at the Prince of Wales hospital, local media reports stated.
Benaud's wife Daphne said the former cricketer was recovering well.
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"At first I was quite concerned but today he's looking unbelievably well," she added.
Cricket Australia has wished Benaud a speedy recovery.
"We wish cricket legend Richie Benaud a speedy recovery after being involved in a car accident in Sydney," CA said in a tweet.