Around 20 of the injured were taken to hospital with head injuries, concussions, broken legs, sprains and other injuries, according to the German Red Cross.
Thrown out of the trailer
A May wagon is a tractor with a trailer intended for people who are going on an excursion on May Day of the year.
The accident happened in the town of Kandern, south of the larger city of Freiburg near the border with Switzerland and France.
A tractor with a trailer apparently came too fast around a left-hand bend and overturned.
This resulted in people being thrown out of the trailer. This is reported by the police.
There were 40 people in the trailer when it overturned. Photos show two rows of benches on the overturned trailer. Several boxes of beer are stuffed into the front of the cart.
According to the police, it is being investigated whether the driver of the tractor has acted irresponsibly.
– The investigation will focus on whether too many people were put on the trolley, says a spokesman for the police
Ambulances and medical helicopters
Both ambulances and a medical helicopter were sent to the scene to collect the injured.
Accidents were reported elsewhere in connection with May Day.
In the southern state of Bavaria, three children aged 5 to 12 and a 52-year-old woman were injured when a maypole fell.
In Tyrol, Austria, a seven-year-old boy was seriously injured when strong winds caused a 30-metre-high corn stalk to overturn.