Mr Brand, 46, noticed the wallaby had a joey in its pouch and tried to save both during the incident on Monday, locals told The Sun.
He managed to rescue the baby but sadly the mother died.
Mr Brand has a luxury cottage in the south Oxfordshire town which has a population of wild wallabies that are believed to have escaped from a private collection more than 20 years ago.
However, the wallaby is believed to have been from a nearby wildlife park.
Locals said Mr Brand was horrified by what happened.
One said: “Absolutely no one is blaming Russell or his dog - it’s just a horrible accident.
“In fact, Russell was the hero because he managed to save the little joey and it could have been far worse if he hadn’t stepped in so quickly.
“He is a very caring man with animals — he has plenty of pets and they’re all his babies. I understand he’s devastated over what happened. It’s really sad.”
Mr Brand regularly shares photographs and videos of his dog on his Instagram.
Beale Park, a wildlife attraction based about 10 miles away in Berkshire, keeps wallabies and locals believe it may have come from there.
Last month, Mr Brand shared a sweet video of his cats trying to stop Bear from eating his food, with one of them pulling his tail.
The dog turns round and looks at it before Russell says soppily: “You all right, Bear? They bullying you?”
The actor has previously described Bear as a “tornado of fur”.