MADRID—Shares in Portuguese and Spanish banks fell sharply a day after Moody's Investors Service downgraded Portugal's sovereign-debt rating to junk and warned that the country may need another round of aid from the European Union.

Shares in Banco Comercial Portugues SA fell more than 5% in Lisbon morning trading, while Banco Esprito Santo SA and Banco BPI SA both were down more than 4%.

For...