Leah Stewart had her arm amputated after being bitten by a suspected great white shark while swimming at Coogee Beach in Sydney's east on June 13.
The mother of one daughter spent a week on life support and had multiple surgeries.
In an update on her condition on Thursday, her brother Josh said the 34-year-old teacher had stabilised and was off the critical list.
"Leah has been brought out from the heavy sedation and is now awake and alert and has been able to speak with our family and her medical team," he wrote on a fundraising page.
"It's amazing to hear from her so much sooner than anyone expected."
Ms Stewart was overjoyed to see her daughter August on Wednesday night for the first time since the attack, her brother said.
"Leah has asked that we share her thanks and appreciation for everyone who has supported her through this difficult time," he said.
Mr Stewart said his sister can't personally respond to the "lovely messages" she has received because her remaining arm is severely injured and she cannot use her hand.
"Her remaining arm has severe tendon and nerve damage, which will require further repair and intensive rehabilitation," he said.
Ms Stewart "still has a long way to go" with an extensive recovery and rehabilitation process ahead, which includes more surgeries in the coming weeks, he said.
"In time, Leah will want to share more of her story," Mr Stewart said.
"She remembers the whole event in detail, but for now is focused on resting and healing."
A fundraiser page set up to fund her medical procedures and aid her family has garnered more than $500,000 in donations.
Ms Stewart's attack reignited calls to cull shark populations to protect swimmers, but NSW Premier Chris Minns has said the great white shark population cannot be targeted as it is protected.
Shark nets, which are temporarily removed during the winter whale migration season, will be reinstalled at the start of September.
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