And the NSW government is not ruling out the measure.
The attack happened about 20-30 metres from shore and between the flags at Sydney's popular Coogee Beach about 11am on Saturday.
The woman, believed to be in her 30s, was airlifted to hospital after being brought from the water by an off-duty lifeguard.
The incident has prompted NSW independent MP Rod Roberts to call for a shark cull in the interests of community safety.
NSW Agriculture Minister Tara Moriarty did not rule it out on Sunday.
"Nothing is off the table in terms of how we keep the community safe," she told reporters.
Shark nets would be installed on September 1 and the government was seeking expert advice from the Department of Primary Industries, Ms Moriarty said.
Mitigation programs included drone surveillance and shark tagging.
"We swim in the ocean with living, breathing animals and we have to share the ocean every day," she said.
Mr Roberts said swimmers needed to be protected.
"We're not talking about culling out on the Great Barrier Reef, just the popular swimming areas around Sydney," he said.
Marine experts and conservationists warn culling is not a sustainable, scientifically grounded solution.
Footage from a Westpac Life Saving Rescue Helicopter showed a large shark swimming close to the shore on Saturday after the attack.
All of Sydney's eastern suburbs beaches remain closed after Randwick City Council made the call to prohibit anyone from entering the surf during the 24 hours following the attack.
The closure included Coogee, Clovelly and Maroubra beaches, and "all other ocean beaches under council management".
As a precaution, Bondi, Bronte and Tamarama beaches were also closed.
Surf Life Saving NSW officials said the woman was taken to St Vincent's Hospital with serious arm and leg injuries but was "semi-conscious and breathing".
Guards stationed at the beach responded immediately, administering emergency first aid and CPR before paramedics arrived, Randwick mayor Dylan Parker said.
The shark involved is believed to be three to four metres long and possibly a Great White, which is a protected species.
SLNSW has sought an exemption from the Civil Aviation Safety Authority to fly drones, Ms Moriarty confirmed.
Lifeguards were seen testing them at Coogee Beach.
"This has been an incredibly tragic event, and looking out here at our beach shut - it's a very eerie environment," local MP Marjorie O'Neill said.
The Department of Primary Industries and Fisheries shark programs leader Marcel Green said Saturday's attack was "unique and different".
"She (the swimmer) was doing everything right but it was just one of those random events and we can never be protected 100 per cent every day, all the time," he said.
About 170 white sharks have been detected by the department's listening stations dotted across the entirety of the state's coastline
The most recent fatal attack in Australian waters was on June 6, when 35‑year‑old diver Daniel Turpin was bitten by a suspected 4.5‑metre shark while spearfishing near Albany in WA.
His death followed those of 38‑year‑old Perth father Steven Mattaboni off Rottnest Island and spearfisher Michael Jensz, 39, south of Cairns in May.
In January, NSW made international headlines after recording four shark attacks in 48 hours.
Two resulted in people being hospitalised in critical condition, while the other two escaped without serious injuries.
Australia has the second-highest number of recorded shark incidents globally, averaging 22 bites per year, according to the Australian Institute of Health and Welfare.
Coogee Surf Life Saving Club will host a community gathering on Monday at 6.30pm.
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