The legislation would require stores to keep tobacco products in cabinets, drawers, under the counter, behind a curtain or in other concealed spots. They could only be visible when an adult is making a purchase or during restocking.
Bloomberg said similar prohibitions on displays have been enacted in other countries, including Iceland, Canada, England and Ireland.
"Such displays suggest that smoking is a normal activity," Bloomberg said. "And they invite young people to experiment with tobacco."
Stores devoted primarily to the sale of tobacco products would be exempt from the display ban.
The mayor's office said retail stores could still advertise tobacco products under the legislation.
The legislation, to be introduced in the City Council on Wednesday, is comprised of two separate bills.
The second, called the "Sensible Tobacco Enforcement" bill, strengthens enforcement of discounted and smuggled cigarettes. It would prohibit the sale of discounted tobacco products, impose packaging requirements on cheap cigars and create a price floor for cigarette packs and small cigars. The city would have the authority to seal premises where there are repeat violations.The bill would also increase penalties for retailers who evade tobacco taxes or sell tobacco without a license.
Bloomberg has backed a number of public health measures, including a crackdown on large sizes of sugary drinks and adding calorie counts to menus. A judge blocked the drinks ban but the city is appealing.