Under the plan, approved by Canberra last week under an exemption to national environmental protection laws, baited drum lines with hooks can be set one kilometer (0.62 miles) off busy Western Australian beaches until April 30.
It follows six fatal maulings off the west coast in the past two years, leading local marine experts to declare it the deadliest shark attack area in the world.
Any shark longer than three meters snagged by the lines and deemed to be a threat -- including great white, bull and tiger sharks -- will be humanely destroyed.
Activists slammed the first killing Sunday, with the Conservation Council warning of a "pretty significant public backlash".
"This is just going to increase the level of public opposition to the shark cull when people see images and hear stories of these sharks being culled," said council director Piers Verstegen.
"It is certainly a sad day for our marine life and for thousands of people in WA opposed to killing endangered sharks," he added.
While sharks are common in Australian waters, deadly attacks are rare, with only one of the average 15 incidents a year typically proving fatal.