Tasmania has recorded its first measles case in four years, a person who recently returned from travelling overseas.

The person, in their late 20s, tested positive on Wednesday and is in isolation in the Launceston General Hospital.

"Contact tracing is under way to identify people who may have been exposed to the case while they were infectious," acting state director of public health Scott McKeown said.

The person briefly spent time at several locations while infectious.

They were at the Launceston Medical Centre from 5.40pm to 6.15pm on Friday, Mowbray Coles from 6.05pm to 6.45pm on Friday.

They were also at the Launceston Respiratory Clinic on Saturday from 11.20am to 12pm on Saturday and the Launceston General Hospital emergency department waiting room from 3.12pm to 6.35pm.

People who were at the locations at those times and have not received two measles vaccines are urged to be alert for symptoms for up to 18 days following their exposure.

Symptoms may include fever, tiredness, cough, runny nose, sore red eyes and a red blotchy rash which appears about four days after initial symptoms.

People who have had two doses of measles vaccine, or were born before 1966, are generally protected against catching measles, the health department says.