7HOFM presenter Anna Dare made the gaffe during a "secret sound" segment on Thursday morning asking "it's not getting stuck in a conveyor belt at a theme park is it? ... Too soon?"
The chief executive of Grant Broadcasters, Grant Cameron, said the unacceptable comment demonstrated a serious lapse in judgment and did not reflect the values of 7HOfm or its parent company.
He confirmed Dare was taken off the air immediately, had been suspended and would be counselled.
"A decision will be made at a later date about when she might return to an on-air role," he said.