Supermarket giant Kroger, which owns Fry's Food and Drug in Arizona, is no longer accepting a popular form of payment at some of its stores.

The company announced this week that it won't take Visa credit cards at 21 of its Foods Co. stores in California, citing high costs associated with the credit card company's interchange rates and network fees.

A Kroger spokesperson tells Bloomberg that the company is prepared to expand the Visa credit card ban beyond California, saying that the amount retailers pay in fees is "out of alignment." Visa said in a statement to CNBC that it's disappointed by Kroger's decision, but says it plans to work for a reasonable solution.

As of now, no such ban has been announced at other Kroger-owned chains, including Fry's. The Foods Co. stores will still accept Mastercard, American Express and Discover credit cards as well as Visa debit cards.