One shopkeeper in the bazaar, who gave his name only as Fazlullah, said: "It was very crowded when the bombing took place. Most of the casualties are shopkeepers and people and children who were selling stuff on the roadside," he said.
"Around 15 shops have been damaged. I saw lots of people killed and injured. I can see human flesh, blood and pieces of metal, wood, clothing scattered around. Everything is bloodied."
Al Jazeera's James Bays, reporting from Kabul, said that Uruzgan provinces is one of the country's most volatile areas.
He said: "The markets located in the area would have been packed with people, increasing the destructive force of the attack."
"It is a volatile area in which previous deadly attacks have taken place."
Bays also reported that an Afghan MP has been kidnapped by Taliban fighters in Logar province, 80km south of Kabul.
"We have the news of this kidnapping confirmed by parliamentary sources," he said.
"However, the Taliban has not yet released any information on the conditions for the release of this MP."
Provincial health chief Khan Agha Miakhail said that of those taken to hospital were four children under the age of 10.
The blast took place less than a week after a suicide bombing at the Indian embassy in Kabul, which killed more than 40 people including four Indian nationals, two of them senior diplomats.
The Kabul bombing was the deadliest suicide attack in the capital since the Taliban were removed from power in 2001.
Also on Sunday, the Taliban said they shot dead two women who they alleged were prostitutes and had worked for the police.
The government, however, rejected that the women were working for the police.
Ismail Jahangir, a provincial government spokesman, said the bodies of the women were found late on Saturday in the central province of Ghazni.
In Nuristan province, four police were missing after clashes with fighters near the eastern border with Pakistan, a governor said on Sunday.
Fighters overran two police posts in days of heavy fighting near the border, said Abdul Aleem, the deputy provincial governor.
Two of the fighters, whom Afghan officials said had attacked bases in Pakistan, were also killed, Aleem said.
He identified them as Chechens but this could not be confirmed.
International and Afghan forces have been engaged in fighting in Helmand province.
The US-led coalition said it had killed 40 insurgents over two days, although the Taliban said it had lost just one man.
Nato-led soldiers were also engaged in heavy fighting in the northeastern province of Kunar on Sunday.
Captain Mike Finney, a spokesman for Isaf, said: "The fighting started early today and it's still ongoing. We have taken casualties."
Aleem said those clashes started with an attack on an Isaf base. The troops responded with air strikes, he said.
"Some homes were destroyed and damaged. There have been casualties among all three sides - the locals, Taliban and foreign forces," he said.
Nine Nato-led soldiers were also killed in Kunar on Sunday.
Another 15 Isaf soldiers were wounded along with four Afghan troops, the force said in a statement.
Officials also said that eight of nine killed were US soldiers under the command of Isaf and the other soldier was working for a separate US-led force.