A fundraiser for a new mother whose arm was amputated after a shark attack has brought in more than $270,000 in less than 24 hours.

Leah Stewart, 35, was swimming between the flags and close to the shore at Coogee beach, in Sydney's eastern suburbs, on Saturday morning when she was attacked by a great white shark. 

Her one-year-old daughter was on the sand with a friend at the time.

Ms Stewart was rescued by off-duty lifeguard Charlie Verco who saw the attack from his paddleboard. She lost consciousness as he paddled her back to shore.

The school teacher lost so much blood in the attack, paramedics had to give her multiple transfusions on the beach, a friend has revealed on social media.

She was airlifted to St Vincent's Hospital in a critical condition and has undergone several operations on her life-threatening injuries, with even more to follow.

Her brother Joshua Stewart created a GoFundMe campaign just before 3pm on Monday to help with her recovery, revealing that her arm had been amputated.

About 18 hours later, the fundraiser had seen significant contributions from concerned community members, with donations ranging from about $20 to $5,000.

In a heartfelt Facebook post, Ms Stewart's friend urged people to donate blood if they were unable to make a financial contribution.

'Leah is a part of my mother's group and is one of the kindest people. We would all sit on the Coogee hill and take turns having swims while the bubs played,' she wrote.

'She was the first one to reach out to anyone she thought was struggling while going through our first year of motherhood together.

'Giving blood is also a great way to honour Leah. 

'She received multiple units on-site of the accident when the chopper arrived, and this contributed to saving her life on the day.'

In the fundraiser, her brother wrote: 'Leah remains in a critical condition on life support and has undergone multiple surgeries in the days after the attack. 

'Tragically, her treatment has required the amputation of her arm, and more surgeries are scheduled for the coming days.'

He said her recovery would be a long process and all donations would go towards rehabilitation, prosthetics and improving her quality of life.

Mr Stewart confirmed his sister was swimming between the flags and close to the shore when the shark attacked, and thanked first responders who helped save her. 

Mr Verco, 25, was paddleboarding about 100m from Ms Stewart when the attack occurred. 

He immediately paddled towards Ms Stewart and helped lift her from the water. 

'The water got very bloody and she got taken under and after a few seconds, popped up again and the shark had let her go,' he told ABC News.

'All I really wanted to do was to go to shore, obviously, but because I was the only one on any craft near her, I was, like, if I don't, I'm not here to help her, no-one is.

'She was lucid enough to say, "Help", and respond to instruction, but she was very much in shock and definitely freaked out and wasn't able to have conversation.

'That was when I was able to actually get close enough to her and get her to grab the front of my board.' 

Mr Verco said he tried to comfort her, telling her 'We're almost ashore' and 'You're doing really well' to take her mind off the severity of her injuries. 

He realised she was too injured to climb onto the board, so he told her to hold onto a drink bottle holder on the front while he paddled. 

'About halfway into shore, she lost consciousness and I had to go grab her by the arm and just keep her head out of the water with one arm and paddle backwards with the other until we got close to shore, where there were lifeguards ready to help.'

Ms Stewart, who has lived in Coogee for several years, swam 50km in November to raise funds for breast cancer research.  

'As a breastfeeding mum, I have a whole new appreciation for these incredible organs and want to do my part in supporting the fight against the most common cancer in women,' she wrote on her fundraising page.

The attack has renewed calls for a shark cull around Sydney's beaches, which followed a series of bull shark attacks in January. 

NSW Premier Chris Minns said the government was exploring a bull shark cull but would not target great whites, which are protected under Australian law. 

'I'm not convinced it would work and we've certainly had no expert evidence suggesting to us that we could ward away great whites from our beaches as a result of a cull,' he said.

'The reality is those sharks may have come from New Zealand or crossed the Pacific Ocean. We haven't received expert evidence or information that a cull would work.' 

Coogee Beach was not being monitored by shark surveillance drones at the time of the attack because the area lies beneath a flight path. 

However, authorities have since granted a special exemption allowing drones to temporarily monitor shark activity. 

The shark that attacked Ms Stewart is believed to have been between three and four metres long.