A person was infectious while travelling on the service on December 28 from Wellington to Picton between 7.45am and 12.30pm, and again on the return trip on Monday between 2.15 and 5.45pm.
They attended the Whare Flat Folk Music Festival from December 30 to January 3 and were also at Dunedin Hospital's ED on December 30 between 9am and 1pm.
Anyone who was in those places at those times should remain isolated unless they've had two MMR vaccinations or are over 50 years old.