Bank of America Corp. is raising interest rates on as many as four million U.S. credit-card customers who carry a balance, becoming the latest bank to crack down on people who don't pay off their bill every month.

Starting with June account statements, any credit-card customer who carries a balance and has an interest rate below 10% will see his or her rate jump into double-digit territory. A company spokeswoman declined to provide an exact number, saying the changes would affect less than 10% of the bank's card customers...