Yes, most financial institutions are required to comply - the following quote came from the Visa Cardholder Information Security Program website, under PCI DSS Compliance:
"PCI DSS compliance is required of all entities that store, process, or transmit Visa cardholder data, including financial institutions, merchants and service providers. The PCI DSS applies to all payment channels, including retail (brick-and-mortar), mail/telephone order, and e-commerce."
See
Visa CISP Overview See also
PCI Security Standards Council However, since banks are highly regulated and regularly/formally examined/audited, they are not usually on the radar by Visa.
Hope this helps some.