The nation's beleaguered banking industry, which has been raising fees and doing away with free services, has a new target: debit-card users.

Bank of America Corp. is laying plans to charge millions of customers a $5 monthly fee to use their debit cards, and other big banks are expected to follow suit. The industry says it needs the fees to recoup revenue it will lose because of new government regulations taking effect Saturday that cap what they can charge merchants for debit-card transactions.

Bank...