The Tasmanian commercial radio presenter who made a joke in reference to the deaths at the Dreamworld theme park has quit her job, according to the station's parent company.

The comments came during 7HO FM breakfast program's "secret sound" segment on October 27, two days after the incident at the Queensland theme park where four people died after a mishap on the Thunder River Rapids ride.

After a crunching sound was played on air, presenter Anna Dare asked: "It's not getting stuck in a conveyer belt at a theme park is it … too soon?"

Ms Dare's co-presenter Mick Newell groaned, prompting Ms Dare to respond: "That's what it sounds like to me when I first heard it, that's the first thing I thought of, I don't like it, it's just a yucky sound."

The station has announced Dare had decided not to return to the role she started in January and intended to take a break from the radio industry.

"Anna Dare has resigned from 7HO FM," general manager Col Taylor said in a statement.

"She thanked the station for its support and the opportunity to return on air, but has decided to take a break from radio."

After the incident station management announced Dare had been suspended from on-air duties, with Mr Cameron issuing a statement saying: "The announcer's remark demonstrated a serious lapse in judgement and we sincerely apologise to our listeners, the broader community and everyone affected by this week's terrible tragedy."

Public servants Kate Goodchild, her brother Luke Dorsett and his partner Roozbeh Araghi were killed alongside 42-year-old Cindy Low when the Thunder River Rapids ride malfunctioned.