Two of the biggest credit-card issuers are tightening lending standards, an unusual move in a strong economy that may signal longer-term concerns about consumers’ financial health.

Capital One Financial Corp. and Discover Financial Services said last week they have become more cautious in how they’re handling credit limits. The two lenders said they don’t currently see signs of deterioration in consumers’ ability to pay their debts but do question how much longer the economic recovery will last.

“In...