This is the single most important practical fact about Woods Hole and it catches visitors out constantly.
The village is tiny, the streets are narrow, and what limited parking exists is either permit-only, metered and short, or reserved for the institutions. The Steamship Authority does not park ferry passengers in the village either: its car parks are in Falmouth, principally off Palmer Avenue, with a shuttle bus down to the terminal. If you are catching a boat, that is where you leave the car, and you should build the shuttle time into your arrival.
The alternatives are better than they sound.
Ride the Shining Sea Bikeway. It runs 10.7 paved miles from North Falmouth to the ferry terminal itself, and arriving in Woods Hole by bicycle removes the entire problem. Bike racks are at the terminal and around the village.
Take the shuttle even if you are not sailing. Seasonal shuttle services run between Falmouth and Woods Hole and are the easy way to spend an afternoon in the village.
Do not improvise a space on a residential street. Enforcement here is consistent, and there is a reason for it: eight hundred people live in a village that receives a large fraction of Martha's Vineyard's annual traffic.