The unnamed hunter, who was pictured with the corpse, reported paid $60,000 for the legal hunt.
It comes months after American dentist Walter Palmer killed Cecil the lion.
There was international outrage after Cecil, a 13-year-old lion, was killed during another legal hunt in July, also in Zimbabwe.
Walter Palmer found out earlier this week that he will not face charges over the shooting.
The death of the elephant also took place during a hunt in Zimbabwe’s southern Gonarezhou National Park.
The Zimbabwe Association of Safaris Operators (Zaso) said the elephant was the largest seen in Zimbabwe in 100 years. Its tusks, which were so large they almost touched the floor, weighed 120lbs.
Zaso chairman Emmanuel Fundira said the hunter should have thought twice before shooting.
Walter Palmer was vilified after being identified as the killer of Cecil the lion and he closed his dental practice in Minnesota temporarily after campaigners gathered outside.
Animal rights charities criticized the decision not to prosecute him.
Earlier this week, rangers at Zimbabwe’s Hwange National Park, where Cecil the lion was killed, discovered the carcasses of 26 elephants killed by cyanide poisoning.
Poachers are known to poison salt pans with the drug in order to steal the elephants’s tusks.
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