Two people were in the helicopter, one of whom was able to leave on foot, while the other was rescued from the wreckage by firefighters, an emergency service spokesperson said.
Both helicopter passengers were injured in the crash, as was the driver of the car hit by the helicopter.
One of the crash survivors had a light head injury, another had a broken thigh bone and the third suffered light injuries.
Footage showed the two-seat yellow helicopter lying on its side with its glass cockpit shattered and its tail smashed over the central reservation beside a motorway bridge.
Dozens of emergency officers were deployed to secure the area. The car's windshield was also shattered and its body showed gashes.
A spokesperson for European Rotors 2023, a helicopter show held from Monday to Thursday at Madrid’s Ifema conference centre, said the helicopter had been flying from Ifema to Cuatro Vientos airfield located south of the city.
According to local media, investigators are looking into whether the crash may have been caused by a technical problem or if the aircraft was driven against a concrete pillar above the motorway bridge by a gust of wind.
Madrid was experiencing moderate winds of around 10mph on Friday morning.
Madrid mayor José Luis Martínez-Almeida praised the pilot for managing to avoid a deadly pile-up on the motorway by landing on the central reservation.
“Although we don’t yet know the exact details of what happened, everything suggests that the skill of the pilot certainly prevented a much greater tragedy,” the mayor said.