Dr Hinds was involved in an accident while providing medical cover at a motorcycle event in the Republic of Ireland.
Minister Hamilton said: “I had the honour of meeting Dr Hinds recently. His skill was undoubted but what shone through was his passion for his work.
“John was extremely well regarded not just within the medical profession, but right across the motor cycling world, where his loss will be greatly mourned.
“My thoughts and prayers are with his family, friends and colleagues at this very difficult time.”