The person spoke to the AP on condition of anonymity because of sensitivity to Smith's medical privacy. The person says Smith will be placed on injured reserve on Wednesday due to a back injury.
Smith, who played through bumps and bruises throughout his three-plus seasons with Cleveland, was inactive for Sunday's game in Pittsburgh.
On Monday, Browns coach Eric Mangini said Smith's injury could be long-term and that it was "possible" Smith would go on IR, joining starting linebacker D'Qwell Jackson, who tore a chest muscle and had surgery.
Smith's agent, Michael Harrison, said Smith will seek a second medical opinion.