"There can't be any more cases like this," said Hinz, adding that the state government would push the Bundesrat (upper house of parliament) to vote for a ban.
Under the plans in Hesse, travelling circuses would be forbidden from keeping elephants, bears or big cats, the Frankfurter Allgemeine Zeitung reported.
The elephant cow escaped from a circus in Buchen, Baden-Württemberg early on Saturday morning and crushed a pensioner against a fence while he was out collecting bottles and cans.
Police are investigating whether the death was caused by negligence on the circus owner's part, although he himself accused animal rights activists of freeing the animal.
Baden-Württemberg has announced a more limited measure to ban circuses from keeping elephents.
But the German Animal Protection Federation wants to forbid wild animals in circuses altogether.
Hinz accused the federal government of "years-long inactivity", doing nothing while the states repeatedly raised the circus issue.
She said that keeping animals in travelling captivity severely limited their movement and opportunity to behave normally.