The 29-year-old woman was travelling with friends in the Kamchatka Peninsula, in far eastern Russia when the attack occurred on Wednesday.
"The woman found herself face to face with a bear while climbing the Tolbachik Volcano with friends," Viktor Roumantsiev of the Russian Foreign Ministry told the AFP news agency.
He added that she was taken to hospital, where she remains in a serious but stable condition. The bear attacked her face and legs, he said.
The group of friends had been hiking in the area without guides, the ministry spokesman said.
The area is believed to be home to around 15,000 brown bears, a species which can grow to be three metres tall when standing, and can weigh up to 700 kilograms.
There have been two bear attacks on humans in the area already this year, reported French radio channel Europe 1, although both of the victims survived.