Early-stage deal talks between Walmart Inc. and Humana Inc. are deepening anxiety in the hospital sector, which already has been grappling with sluggish growth and competition from cheaper health-care options.

Hospitals have been eyeing Walmart nervously for years as it advances into health care, seeking to leverage its enormous purchasing heft, physical reach and focus on price. The Bentonville, Ark., retailer already operates pharmacies and primary-care clinics and plans to begin offering lab-testing services. It has also...