Visa Inc. has a new offer for small merchants: take thousands of dollars from the card giant to upgrade their payment technology. In return, the businesses must stop accepting cash.

The company unveiled the initiative on Wednesday as part of a broader effort to steer Americans away from using old-fashioned paper money. Visa says it is planning to give $10,000 apiece to up to 50 restaurants and food vendors to pay for their technology and marketing costs, as long as the businesses pledge to start what Visa executive Jack Forestell calls a “journey to cashless.”

“We’re really viewing this as the opening salvo,” said Mr. Forestell, Visa’s global head of merchant solutions, of the potential total $500,000 commitment.

Consumers at those stores would be able to pay for goods or services only with debit or credit cards or with their cellphones. In exchange, Visa is offering to pay for upgrades to merchants’ technology at the checkout line so that they can accept contactless payments, such as Apple Pay . The $10,000 incentive can also help cover some of the merchants’ marketing expenses.

Visa will pick the participating merchants from an application process that starts in August. Online-only shops are excluded.