Hospitals are pushing back against the Trump administration’s new health-pricing disclosure rule, with the industry planning a legal challenge to block it.

The final rule, released Friday along with a proposed rule aimed at insurers, would require hospitals to disclose the secret rates they negotiate with insurers for all services, including supplies and care provided by doctors who work for the facility. If they take effect, the requirements would be a major change for the health industry, where the negotiated prices are...