His sister Kalli Sandberg announced the transfer from Marin General Hospital to an undisclosed San Francisco facility on Monday via the Web site CaringBridge.org, a free site that connects families and friends of patients with serious health problems.
"Gunnar is doing amazingly well," his sister wrote. "I am proud of my little brother."
She said Gunnar, who is 17, is not yet speaking but smiled while watching the movie The Hangover.
"The last 72 hours, Gunnar has made dome major improvements. He is more awake and aware of his surroundings, but with being more awake he is starting to become sad and frustrated about the situation," Kalli Sandberg said.
The teen was struck in the head with a ball hit with a metal bat, and was placed into a medically induced coma. A portion of his skull was removed to reduce swelling in his brain.
The incident has sparked a debate over whether metal bats are more dangerous than wooden bats.
The 10 high schools in the Marin County Athletic League agreed to suspend the use of metal bats for the rest of the season, including during tournaments and playoffs.
Assemblyman Jared Huffman said he plans to introduce legislation banning the use of non-wood bats at high school baseball games in California until safety standards are developed and implemented.
Fundraising efforts for the Sandberg family have included selling "Got Wood" T-shirts and wristbands. Donations to the family may be made at the Gunnar Sandberg Fund at the Bank of Marin.