Officials say the attacker drove a 4×4 vehicle into the market in Orgun district and detonated the explosives.
The market was full of people doing their shopping for the Muslim festival Ramadan at the time of the attack.
No group has claimed the attack, but Taliban insurgents said they had not carried it out.
“We clearly announce that it was not done by the Mujahedeen of the Islamic Emirate of Afghanistan,” Taliban spokesman Zabihullah Mujahid was quoted as saying by Reuters news agency.
Eyewitnesses and medical staff said local hospitals were overrun with casualties after one of the deadliest attacks in months in Afghanistan.
The eastern province of Paktika shares a border with Pakistan’s restive and volatile tribal areas.
Orgun is one of Paktika’s safest areas, though members of the Haqqani militant network are thought to have a presence there.
A spokesman for Afghanistan’s defense ministry said that most of the 89 bodies recovered from the rubble were women and children.
Some 42 injured people have been taken to hospital.
Most of those killed were shopkeepers and people doing their Ramadan shopping.
One man who witnessed the attack said the blast was huge and destroyed dozens of cars and shops.
Eyewitnesses say police and security forces pursued the attacker before he entered the market.
One doctor at Orgun hospital, said it had become overcrowded with casualties.
“We have got children, men and women injured and dead,” he said.
The attack occurred hours after two men working for the media team of outgoing President Hamid Karzai were killed by a roadside bomb in Kabul.
The Taliban said it had carried out the attack, which targeted a vehicle carrying employees of the presidential palace to work.
It comes days after Afghanistan’s two presidential candidates reached a deal to resolve a dispute over the results of last month’s presidential election.
The contenders, Abdullah Abdullah and Ashraf Ghani, agreed to accept the outcome of a vote audit after earlier allegations of voter fraud.
The dispute had revived fears for Afghanistan’s stability after the withdrawal of US-led forces later this year.
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