Article I, Section 10, Clause 1: No State shall enter into any Treaty, Alliance, or Confederation; grant Letters of Marque and Reprisal; coin Money; emit Bills of Credit; make any Thing but gold and silver Coin a Tender in Payment of Debts [emphases added]; pass any Bill of Attainder, ex post facto Law, or Law impairing the Obligation of Contracts, or grant any Title of Nobility.
Insights, corrections welcome.
Originally, our paper money was a certificate, essentially an IOU for a certain amount of gold or silver. Paper is much easier to carry.
When we went off the gold standard, the paper itself became the money, instead of a certificate representing the actual money.
Besides, the section you cited specifically states that it is related to the states. Our currency is Federal.