The Tasmanian radio host who made a shocking joke about the Dreamworld tragedy on air has resigned.

Anna Dare, who co-hosted the 7HOFM breakfast show with former My Kitchen Rules contestant Mick Newell, was offered the chance to return to the show but turned it down.

"She thanked the station for its support and the opportunity to return on air, but has decided to take a break from radio," CEO of Grant Broadcasters, Grant Cameron said in a statement to news.com.au.

Dare inappropriately referenced the theme park incident in which four people were killed during a Secret Sound segment in late October.

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"I really don't like it," Dare said after hearing the sound that listeners had to guess in order to win $140, "it's violent sounding".

"It's not getting stuck in a conveyor belt at a theme park is it? Too soon?"

Dare's co-host sounded shocked by the comment and simply responded with a sigh.

"That's what it sounds like to me when I first heard it," Dare protested, "that's the first thing I thought of".

Dare was taken off air shortly after making the comment and was suspended by 7HOFM and its parent company, Grant Broadcasters.

"The announcer's remark demonstrated a serious lapse in judgment and we sincerely apologise to our listeners, the broader community and everyone affected by this week's terrible tragedy," the CEO of Grant Broadcasters said at the time.

The search is now on to find a replacement host to broadcast alongside Mick Newell who has been hosting the 7HOFM breakfast show for more than three years.

Newell was only joined by Anna Dare in January this year.

Last month Dare told The Mercury that hosting the breakfast show was her "dream job".

"We moved from the Gold Coast to Hobart specifically so I could take this job and I haven't regretted it for a minute," she said.

Speaking about their on air partnership, Newell said they "plan nothing" before each show.

"We don't script anything, we just try to come in with fresh heads and a few stories up our sleeves and jump in - and it works," he said to The Mercury.