What is the absolute minimum garage door size that will still fit a (small) car?
The door doesn't need to be much wider than the car - 10cm or 4 inches either side of the mirrors should be plenty in a straight line.  But it's conventional to make the door very nearly as wide as the garage, for ease of access especially if you need to turn.

I've got a fairly typical UK family size car, and it's just under 1.8m including mirrors.  Even a modern supermini isn't much narrower than this. I suggest you pick a car of the size you've got in mind, and Google that model plus "dimensions".  Then you have to estimate how precisely you can line the car up.  With a line marked on the ground, and leaning out of the window, I know I can get to within ±2 cm on side-to-side positioning, lined up straight, but it's slow and boring (this is lining a van up to an awning). So I've increased by a factor of 10 for safety/convenience margin.  

This would lead to 2 m as a minimum width for a fairly normal car.  This would feel quite tight but be doable.  You would of course have to have the garage wider inside to allow opening the doors.  Smaller cars can need more width as they're often 3-door, which means bigger doors; this effect can be bigger than the reduction in car width.