The case flew from Rotorua and arrived in Blenheim on Thursday. They were tested upon arrival after developing a sore throat.
"The initial test, including a follow-up swab, returned a weak positive result."
The ministry said the case is now isolating awaiting the results of further testing.
The case is considered low risk, due to their likely late stage of infection.
The ministry said initial case interviews suggested the case was linked to the Te Awamutu cluster.