Hildur Runa Hauksdottir is trying to stop the aluminium producer Alcoa building a smelter and power plant in the area above Vatnajokull in east Iceland.
Bjork, who has recently given birth to her second child, was one of the first critics of the huge scheme when it was proposed almost three years ago.
Now Ms Hauksdottir, who helped her daughter produce her first record at the age of 11, is hoping her action will mobilise opposition to the project.
"I'm more optimistic now than I was at the start of the hunger strike," she said.
"People are pledging their support and for me that gives me a lot of strength.
"I don't believe that Alcoa or the Icelandic Government should underestimate the will of the Icelandic people."
Unemployment
Alcoa and the Icelandic Government signed a declaration of intent to build the power plant and smelter in July.
The Karahnjukar Hydropower Project is expected to provide 2,000 construction jobs and up to 1,000 permanent posts in an area of Iceland that suffers from high unemployment.
But environmentalists say the development will ruin the wilderness area above Vatnajokull - Europe's largest glacier.
In June, the World Wildlife Fund called on Alcoa, which has 129,000 employees around the world, to pull out of the plan.
Wade Hughes, member of Alcoa's Iceland project team, has maintained that the project would only alter a "relatively small" part of the wilderness area.
Mr Hughes has also spoken to Ms Hauksdottir about her hunger strike.
"I said to her that we're very sorry to hear that and hope that she would stop," he said.
"If this project goes ahead, we welcome the opportunity to work with supporters and critics alike."
Ms Hauksdottir has been surviving on tea made from Icelandic thyme and yarrow since beginning her hunger strike.
"I haven't decided how far to go," she said. "It might take another week."