The Glasgow Warriors forward will sit out the next autumn Test match at home to Portugal on Saturday.
Cummings was sent to the sin-bin for a "croc roll" tackle on Franco Mostert's lower limb only 10 minutes into the 32-15 defeat at Murrayfield.
An initial yellow card was upgraded to red, meaning Cummings spent 20 minutes on the sidelines according to a recently introduced new ruling.
Tuesday's independent disciplinary committee decided the red card was justified for foul play but "determined that, whilst reckless, the low-range entry point of two weeks was appropriate with the full 50% mitigation applied".
Cummings benefited from "an exemplary disciplinary record, good conduct and having shown remorse".
Scotland were already going to be without three other Glasgow forwards - Jack Dempsey, Max Williamson and Gregor Brown - through injury against Portugal.
Warriors hooker Johnny Matthews and Scarlets prop Alex Hepburn were called up as replacements.