The Petrel began to tilt to one side at Imperial Dock in Leith just after 08:30.
The vessel is thought to have been dislodged after high winds with images showing the vessel leaning at a 45-degree angle.
The Scottish Ambulance Service said it had dispatched five ambulances, an air ambulance, three trauma teams and a special operations team.
1. Emergency services have been called to a dry dock after a ship partially toppled over.
The Scottish Ambulance Service sent five ambulances, an air ambulance, three trauma teams and other resources to the scene, while the fire service also attended. Photo: Andy O'Brien
2. Emergency services at Imperial Dock in Leith
Emergency services at Imperial Dock in Leith, Edinburgh, where a ship has become dislodged from its holding and is partially toppled over. Picture date: Wednesday March 22, 2023. Photo: Andrew Milligan
3. A ship named Petrel has become dislodged and tipped over at an angle.
Pictures posted on social media show the vessel leaning at a 45-degree angle. Photo: Andrew Milligan
4. The scale of the tilt
Emergency services at Imperial Dock in Leith, Edinburgh, where a ship has become dislodged from its holding and is partially toppled over. Photo: Andrew Milligan