Labor would also task the Productivity Commission with the first significant review of the private health system in 20 years to improve the value, quality and affordability of health insurance.
"Under the Liberals, it will be their private health insurance business as usual, prices going up and up and up, and Mr Turnbull will give them a (business) tax cut," Mr Shorten told reporters in Melbourne on Sunday after touring a private hospital with his health spokeswoman Catherine King.
Senior Labor frontbencher Anthony Albanese told Sky News there was increasing concern among families that private health insurance was serving the interests of "profits rather than patients".
But Prime Minister Malcolm Turnbull described it as "policy on the run".
"These are private companies. They're in a very competitive market. The reality is Labor wants to destroy private health insurance," he told ABC television.
Health Minister Greg Hunt said Labor's announcement was a "smokescreen" to distract from its plan to dismantle the system.
"Labor is putting private health insurance at risk. Australians could miss out on the new healthcare and latest medical treatments being developed," he said in a statement.
"Furthermore, a collapse in the private health insurance sector would see public hospital waiting times blow out."
Health insurer NIB chief executive officer Mark Fitzgibbon said Labor's proposal was a "dreadful overreaction".
"That a future government would seek to set prices in any competitive market is absurd," he said in a statement.
"This may be politically popular but it's an affront to how the free market operates. What next? Food, clothing, car insurance, school fees and petrol?"
The Australian Private Hospitals Association warned a cap could result in insurers limiting benefit payments.
"The easiest way for funds to do this would be to cut the amount they spend on medical "no-gaps" schemes," its CEO Michael Roff said.
However, the Public Health Association of Australia welcomed the Productivity Commission review.
"The reality is that premiums have been going up exponentially and there have been a plethora of 'junk policies' that deliver very little for individuals but huge profits for the private insurance companies while effectively undermining Medicare," it head Michael Moore said.
Consumers Health Forum boss Leanne Wells also supported steps to improve health insurance affordability, saying it continued to be a double-edged sword for many consumers.
"On top of their rising health insurance premiums, they continue to face out-of- pocket costs," she said.