Gold panning is not permitted on NRW-managed land because of the potential damage to river ecosystems.
The environment body said the excavation of gravel and the removal of minerals could disturb riverbeds, impacting habitats that wildlife rely on.
It said that although many were unaware of the repercussions, gold panning could lead to prosecution and sentencing “where it risks disturbing spawning fish and impacting river habitats”.
It also said Wright, from Henley On Thames, Oxfordshire, had been sentenced for similar offences in May 2022.
NRW manager for north-west Wales, Euros Jones, told BBC Radio Wales Breakfast that gold panning was “damaging” and could lead to a “concerning environmental cost”.
Jones said Dolgellau “has a history of gold mining” and very small specks of gold could be found among “a lot of gravel”.
“There is a romance around the gold, and it does attract people to the river because it is known for this,” he said.