A 17-year-old female passenger is in a critical but stable condition in Ninewells Hospital following the crash on Camperdown Park's, Main Drive.
The 17-year-old female driver off the red Ford Ka and a 19-year-old male passenger sustained minor injuries.
The incident happened at about 22:10 on Wednesday.
Police Scotland has appealed for information from anyone who witnessed the crash or who was in the area at the time.
Three teenagers have been injured, one seriously, after a car they were travelling in collided with a tree in a Dundee park.