Warner Bros Discovery (WBD) says it will issue refunds to subscribers after the service is shut down on 30 April.
The head of CNN+ has resigned and hundreds more workers could be at risk of losing their jobs.
This week, $50bn (£38.4bn) was wiped off the stock market value of streaming giant Netflix after it revealed a sharp fall in subscribers.
CNN+ was launched on 29 March in an attempt to bring in revenues from news streaming subscriptions.
The company spent as much as $300m on developing the service but it got off to a slow start, attracting just 10,000 viewers a day, according to reports.
Earlier this month, WBD became CNN's parent company with the completion of the merger of media company Discovery and telecom giant AT&T.
Chris Licht, incoming chief executive of CNN, said the business "will be strongest as part of WBD's streaming strategy which envisions news as an important part of a compelling broader offering along with sports, entertainment, and nonfiction content".