Officers from Derbyshire Roads Policing Unit said motorists should slow down and drive to conditions after the incidents at Ripley and Mickleover.
The unit tweeted: “The snow and ice may have gone but it's still raining. The road conditions are far from optimum.
"So please slow down and avoid crashing like these drivers did.
"Minor injuries only. Citroen on the A38 Ripley and Peugeot on the A516 Mickleover.”