[twoodfin]

That's about checkout fees, not minimum charge amounts. Minimum charge amounts used to be forbidden by basically every merchant agreement, but thanks to Dodd-Frank and a lot of retailer lobbying, such contact terms are now illegal. Card issuers must allow a restriction on charge amounts (no more than $10 IIRC) if the retailer so desires.

[mikenon]

You're right. I meant to include Visa's complaint form, https://usa.visa.com/checkoutfees/contact.jsp which mentions the right for US retailers to set minimums up to $10.

It is worth noting minimums can not be set for debit card transactions.