Shares of Capital One Financial Corp., American Express Co. and other US banks sank after President Donald Trump called on credit-card companies to cap interest rates at 10% for a year, a move that could wipe out billions in profits for one of the banking industry’s biggest businesses.

Trump called for the cap on Friday, without detailing how the plan would be implemented, while Wall Street analysts said such a move would require legislation and has slim odds of getting clearance.

Separately, Mizuho analyst Dan Dolev said Trump’s call for a 10% cap could “have major positive ramifications” for buy-now-pay-later and personal loan providers if banks pull back from lower-FICO borr...