The team says Parsons sustained a concussion and whiplash.
Parsons will enter the NBA’s concussion protocol and won’t travel with the Hawks for Friday’s game at San Antonio.
The Hawks provided no additional details on the accident.
Parsons is in his first and likely only season with Atlanta, which acquired him from Memphis last summer in a trade of overpriced players.
The 31-year-old Parsons is making more than $25 million in the final year of his contract. He has played just five games for the rebuilding Hawks, averaging 2.8 points.
The Associated Press contributed to this report.