She tried to fend it off with a broom but had to crawl to safety.
Her son called the police who used pepper spray to subdue it. Mrs Johnson was taken to hospital and the kangaroo was later trapped by rangers.
Red kangaroos are the world's largest living marsupial. Named for their ginger fur, they can weigh about 90kg (200lb), grow as tall as 2m (6ft 7in) and jump more than 9m (30ft).
"I thought it was going to kill me," Phyllis Johnson told the Courier-Mail newspaper from her hospital bed following the attack in the outback town of Charleville.
"It was taller than me and it just ploughed through the clothes on the washing line straight for me.
"I happened to have a broom nearby and I just started swinging at it. I bashed it on the head but it kept going for me. Not even the dog would help, it was too frightened."
'Unusual call' Mrs Johnson was forced to crawl into her home and alert her son who also tried to persuade the animal to go away before calling the police.
Bruised and bleeding, she was subsequently admitted to hospital.
"My son made me. I'm OK, although the 'roo took a chunk of flesh out of my leg and there's a chance they'll have to operate," she said.
The kangaroo lunged at two police officers before wildlife rangers were able to trap the kangaroo.
The animal is being examined by a vet before a decision is made about its future.
"It's one of the many unusual calls we get out here," said senior sergeant Stephen Perkins, head of police in Charleville.
Mrs Johnson said she had always enjoyed the kangaroos, and used to feed them bread.
"They've always been so gentle," she said.
"They weren't as big as that one though and they've never gone for me like that. This one seemed to target me, it was putting its feet into me and kicking."