A $140 million Arizona development is banning residents from bringing their own cars in favor of scooters, bikes and ride-sharing, testing demand for a new type of walkable neighborhood.

The 1,000-person rental community, which broke ground this month in Tempe, won’t allow residents to park cars on site or in the surrounding area as a term of their leases. The founders say it will be the first of its kind in the U.S.

The...