Amazon.com Inc. is positioning Alexa, its artificial-intelligence assistant, to track consumers’ prescriptions and relay personal health information, in a bid to insert the technology into everyday health care.

Seattle-based Amazon says Alexa can now transfer sensitive, personal health information using software that meets health-privacy requirements under federal law. Five companies, including insurer Cigna Corp., diabetes-management company Livongo Health Inc. and major hospital systems, said they developed new Alexa features...