A new mum whose arm was amputated after a shark attack is at serious risk of infection with extensive open wounds, her family has revealed.

Leah Stewart, 34, was swimming near 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.

She was given multiple blood transfusions on the beach before being airlifted to St Vincent's Hospital in a critical condition.

The school teacher's arm was so badly damaged that surgeons had to remove it.

Her brother, Joshua Stewart, has now revealed on GoFundMe that she is still on life support and underwent another complex operation with multiple specialists on Wednesday.

He wrote: 'Given the extensive open wounds contaminated with sand and debris, the risk of infection is extreme.'

'Please pray for her during her continued surgery and for her body to heal without infection.'

He said their mother is a registered nurse who has been by Ms Stewart's side in the intensive care unit.

Ms Stewart's partner Fernando, who was presenting at a conference overseas when the attack took place, has arrived back in Australia to be by her side.

Her brother thanked Ms Stewart's friends for making a playlist of her favourite songs to play in her hospital room. 

'We’re currently printing out photos to put into her hospital room to surround her with positive memories, for when she becomes conscious,' he said.

Mr Stewart thanked friends and community members who donated to the fundraiser and dropped off food, nappies and supplies for the family.

'We’ve been blown away by the support, care, love and generosity we’ve received for Leah,' he wrote.

'Thank you all so much for your prayers, words of support, care, generosity and kindness.'

'Your love, concern and help has made a world of difference to giving Leah and her little family some stability and hope for her recovery.' 

The fundraiser generated more than $420,000 in just three days.

Ms Stewart was swimming between the flags and close to the shore when the shark attacked.

She was rescued by off-duty lifeguard Charlie Verco, who ws 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 previously told the ABC.

'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. 

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

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.