The explosion went off in the town of Gereshk in Helmand province, the world's largest poppy-growing region and site of the country's worst violence this year.
Gereshk district chief Abdul Manaf Khan said about 28 people were killed, saying 13 police had died and about 15 civilians. Dr. Tahir Khan said 23 people were killed and 59 wounded.
The blast came just before evening prayers in this Muslim country, near a taxi stand, Khan said.
Taliban militants have set off a record number of suicide blasts this year - more than 100 through the end of August - but few are as deadly as the Helmand attack. The Taliban typically target international and Afghan military and police forces.
Earlier in the day, a spokesman for the military group said the Taliban would consider negotiating with the Afghan government, but complained that no direct offer has been made by President Hamid Karzai's administration.
"If Karzai and his government ask directly for negotiations, the Taliban would consider that offer," Qari Yousef Ahmadi said by phone from an unknown location.
Ahmadi's comments come a day after Karzai reiterated an offer to negotiate with the hard-line fundamentalists, but added, the fighters "don't have an address" or a telephone number. "Who do we talk to?"
Ahmadi, however, said the militants were easy to contact if government officials wanted to talk. He noted that South Korean officials flew into the country and quickly contacted the Taliban for negotiations over the fate of South Korean hostages last month.
"Whenever the Afghan government wants to hold negotiations, the Taliban is in Afghanistan," he said.