In a statement, Sarah Leo says the situation is being well-managed by the public health office of the Nunatsiavut Department of Health and the Labrador Grenfell Health Authority.
As of mid-May, 14 people had been diagnosed with the infectious disease in Nain since last October.
Two more cases have been reported in other parts of Labrador.
Leo said in her statement that a petition circulating over the past week calling for widespread testing of residents and visitors has added to fear and confusion around the outbreak.
She said health professionals do not feel community-wide testing for tuberculosis is necessary, but the health authority will now hold an open clinic once a week to provide information and assessments to concerned residents.