In the interview, the woman pleads for help and says all of the hostages are sick.
CBS said it arranged the telephone interview with a Taliban commander.
The Afghan government, meanwhile, says Taliban militants have extended a deadline to negotiate the release of the hostages.
The French AFP news agency quotes Wahidullah Mujadadi, the head of the Afghan government delegation negotiating with the kidnappers, as saying the deadline is now noon local time July 27.
Mujadadi says the government is doing its best to win the hostages' release.
Officials in Seoul have condemned the killing on July 25 of one of its citizens by the captors -- a priest and leader of the Christian volunteer group.
The South Korean government called the execution "an unforgivable atrocity."
Foreign Ministry spokesman Cho Hee-yong said Seoul has renewed its calls for the Taliban to immediately release the other 22 South Korean nationals, who have now spent a full week in captivity in Afghanistan's central Ghazni Province since being taken from a bus on the Kabul-to-Kandahar highway.
The government in Seoul rejected earlier reports that some of the hostages had been released.
Senior Envoy Dispatched
In a telephone conversation today, South Korean President Roh Moo-hyun and his Afghan counterpart, Hamid Karzai, agreed to further cooperate toward the captives' safe and quick return, Roh's office said.
South Korea has dispatched a senior envoy -- Baek Jong-chun, chief presidential secretary for security affairs -- to Afghanistan to participate in the ongoing negotiations with the Taliban kidnappers.
Before departing for Afghanistan, Baek pledged that the kidnappers "will be held accountable for taking the life of a Korean citizen."
"The Taliban are not united among themselves. Some of them say they want their people [in exchange for the hostages], while others want money." -- Ziya Wali, assistant to Ghazni's governor
He also offered "heartfelt condolences" to the family of the victim, who was identified as 42-year-old pastor Bae Hyung-kyu.
Bae's body was found with multiple bullet wounds.
Bae and the other hostages -- mostly women -- were reportedly volunteers on a church-backed humanitarian mission in Afghanistan to deliver aid and medical care.
Negotiations began shortly after their abduction on July 19. Their captors have issued numerous deadlines in connection with what officials say have been inconsistent demands. They announced they would kill the hostages if troops surrounding the area tried to rescue them by force.
News agencies have reported that the kidnappers sought to exchange the hostages for an equal number of Taliban prisoners.
"The Taliban are not united among themselves," Ziya Wali, an assistant to Ghazni's governor, told RFE/RL from Ghazni. "Some of them say they want their people [in exchange for the hostages], while others want money."
At least one Taliban source also demanded that South Korea pull its troops from Afghanistan.
Seoul has reaffirmed that it intends to withdraw all of its troops -- around 200 noncombat engineers and medical staff -- by the end of this year, as previously scheduled.