Health Minister Lizzie Nkosi said the latest case involves a man who had travelled to the United States in early March.
Results of his blood tests came positive on Monday, together with those of 62 other Swatis who had presented themselves to health facilities with symptoms.
"The patient's condition is stable and contact tracing has begun on all people who may have had contact with the patient," Nkosi said on Monday.
The results for the other 62 patients showed that they did not have the disease, which is caused by coronavirus.
Nkosi emphasised the importance of personal hygiene, self-isolation if feeling unwell and minimising unnecessary travelling.