Authorities said it happened at about noon in Slidell, northeast of New Orleans.
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According to the sheriff's office, the man's wife told deputies that she was inside her home when she heard commotion.
When she stepped outside, she saw a large alligator attacking her husband, officials said.
The woman ran to help her husband. Once the attack was over, she pulled him out of the water and ran inside to get first aid supplies.
When she realized the severity of his injuries, she got into her boat and went to higher ground, approximately a mile away.
The sheriff's office said that when she returned home, her husband was no longer lying on the steps.
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Authorities used high water vehicles and flatboats in an attempt to find him, but so far, his body has yet to be found.
The attack is still under investigation and deputies said they had no further information to offer at this time.
Sheriff Randy Smith is warning residents to be extra vigilant with walking in flooded areas as wildlife has been displaced as well during the storm. Alligators and other animals may move closer into neighborhoods.
HURRICANE IDA COVERAGE: