Tricky, but I think it should be doable. You need a lot of zoom and a lot of infrared light so that you can limit the shutter speed to something really fast in order to capture the plates without blur or washout from the car's headlights at night. The cam will not be able to see other objects well at night due to the very fast shutter speed you will need to set, so do not expect it to be a general purpose night cam.
A fairly good inexpensive choice is Hikvision DS-2CD2T32-I8 with a 16mm lens. Here is someone's video of using this cam for license plate capture:
Alternatively there is the DS-2CD2T12-I8 which is 1.3MP and is supposed to perform better in low light. It would probably do a comparable if not better job, but there is only one seller on aliexpress claiming to have it and they don't have the best rating.