A woman who was bitten by a shark more than a week ago while swimming at a popular Sydney beach has woken briefly from an induced coma, her family has said.

Leah Stewart, 34, was attacked by a shark on Saturday 13 June at Coogee Beach, suffering multiple bites on her arms and legs and extreme blood loss.

The mother of a one-year-old girl was taken to hospital in a critical condition and underwent several surgeries including her arm being amputated.

On Tuesday, her brother said doctors had reduced Stewart's medication so she could wake up briefly from an induced coma. She said "I love you" to her mum and partner who were both by her bedside and asked if her daughter was ok.

"This is a lot faster than anyone expected, and for us this feels like a miracle and is everything so many of us have hoped and prayed for over the past week," Joshua Stewart posted in an online message to his sister's supporters.

He said she remains in intensive care and had five days of surgery in the past week, with more scheduled in the coming weeks.

"Leah has a long road ahead and still remains in critical care, but this is such a positive first step and gives us hope for Leah's long term recovery."

Stewart, who works as a teacher, had gone to Coogee Beach on Saturday morning for a swim and was in the water close to the shore when the attack happened.

There have been a spate of shark attacks in Australia this year, with four attacks in a two-day period in January including a young boy who was bitten at a Sydney beach and later died from his injuries in hospital.

Last month, there were two fatal shark attacks with one man killed by a shark in Queensland while spearfishing and in Western Australia, father-of-two Steven Mattaboni, 38, died after he was bitten by a 4m (13ft) shark.