The eight-month-old victim is the cousin of another baby girl who was the first in the area to be discovered with the crippling P1 polio virus, they said.
"I can confirm the second P1 polio case in Swat," Waheed Khan, deputy director of the immunisation programme, told AFP.
"We don't know yet whether the infant girls caught the virus in Swat or elsewhere," Khan said.
"We are launching another door-to-door vaccination campaign from July 28-30 and a separate special vaccination will be carried out in Swat, but it depends on peace in the area."
The military has been fighting rebels led by pro-Taliban cleric Maulana Fazlullah in the scenic area since October, preventing inoculation teams from reaching children in some parts of the valley.
The government in May signed a peace deal under which the militants agreed not to block polio vaccination drives and other health initiatives.
But workers were still not able to carry out vaccinations in militant stronghold areas where some 110,000 children live.
The World Health Organisation recently listed Nigeria, India, Pakistan and Afghanistan as the only countries in the world where polio is endemic.