Nottinghamshire Police named 21-year-old Todd as the victim of an accident near Normanton-on-the-Wolds on Wednesday.
Police said Todd was found inside a Citroen C3 shortly before 6am and was pronounced dead at the scene.
The Championship club said Todd, who had played for the senior team in the British and Irish Cup last season, had just finished a degree in sports therapy at Coventry University.
They said in a statement: "He was an exceptional talent and a highly-valued member of the squad, and he will be missed by all of those that knew him. Our thoughts are with Mitchell's family and friends at this difficult time."
Todd qualified for Scotland through his Edinburgh-born father and had also represented Scottish Exiles from under-17 to under-20 level. He won 10 Scotland Under-20 caps and played in the IRB Junior World Championship.
Rob Brierley, the Scottish Rugby Union's performance development manager for Exiles, said: "Mitch was a quiet, sensitive bloke with a real steely determination never more evident than on the rugby pitch. He was a real athlete, somebody who was late to the game and was developing all the time."
The SRU added: "Scottish Rugby extends its sincere condolences to all Mitchell Todd's family and friends."
- Nottinghamshire Police