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.
5. Emergency services at Imperial Dock in Leith,
Emergency services at Imperial Dock in Leith with a multi agency response to the incident. Photo: Andrew Milligan
6. Emergency services at Imperial Dock in Leith
The incident sparked a a multi-agency response, with the Scottish Ambulance Service and Scottish Fire and Rescue also in attendance Photo: Andrew Milligan
7. Emergency services at Imperial Dock in Leith
Emergency services at Imperial Dock in Leith Photo: Andrew Milligan
8. Scotland's Charity Air Ambulance leaves Imperial Dock in Leith
Scotland's Charity Air Ambulance leaves 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