Regardless of how small the load is on the panel, does the NEC mention a minimum allowed size for the main circuit breaker of an electrical panel? Thank you.
Well, since MLO panels are commonplace, I'd have to say zero...
Even when a service panelboard is the item of issue, the NEC only specifies the minimum equipment rating, not the main circuit breaker rating. That is determined by the calculated load.
That is a little like asking if it is permissible protect a conductor usually rated for 100 amps with a 15 amp overcurrent device (or even less).
One difference is the conductor could have adjustments applied to it in some circumstances and have it's ampacity reduced - but panelboards don't get ampacity adjustments that I am aware of.