Tesla Motors Inc. next year will stop providing unlimited free access to its fast-charging stations for new buyers of its electric vehicles, a move intended to help pay for the charging network and the launch of a cheaper and higher-volume electric sedan.

Tesla has gained notoriety for free access to proprietary stations that can recharge its $66,000 and up cars in far less time than a conventional charger. While the company’s investment in the “Supercharger Network” has been steep, it considers the cost a replacement for...