The suicide attack happened in Lashkar Gah, the capital of opium poppy-rich Helmand province, as spectators were leaving a wrestling match at the stadium, provincial governor spokesperson Omar Zwak told AFP.
There was no immediate claim of responsibility for the attack, which Zwak said killed at least 13 people and wounded 45 others, including children.
Helmand police spokesperson Salam Afghan had earlier given a lower toll of 10 dead and 35 wounded.
Afghan officials often give conflicting figures in the wake of attacks.
"The suicide bomber detonated his car bomb as spectators were leaving the stadium," Zwak said.
"The bomber wanted to go inside the stadium but he was identified by the police and he detonated himself."
Local officials were at the match, which witnesses said had been held as part of celebrations for Nawrooz, the Persian new year holiday that some fundamentalist Muslims consider un-Islamic.
Agha Mohammad, a 25-year-old shopkeeper from Lashkar Gah, was among the spectators leaving the stadium when the blast happened.
Suicide bomber kills at least 26 in Kabul
"Four of my family members were martyred and three others were wounded," a sobbing Mohammad told AFP at the hospital run by the Italian NGO Emergency.
Photos posted on Twitter purportedly of the explosion showed a huge fire and a thick plume of black smoke rising into the sky.
"We heard a loud explosion from our surgical centre in the city, Emergency tweeted.
"35 wounded already taken to our hospital, another 4 were dead on arrival."
President Ashraf Ghani, whose government has been lambasted for its inability to protect ordinary Afghans, condemned the attack against "innocent people", according to a statement.
Helmand is largely controlled by the Taliban, which is under growing pressure to take up Ghani's offer of peace talks to end the 16-year war.
So far the Taliban, Afghanistan's largest militant group, has given only a muted response.
The attack caps a bloody few days in Afghanistan as Taliban and Islamic State militants ramp up attacks even before the official start of the spring fighting season.
In Kabul on Wednesday a suicide bomber blew himself up among a crowd of people celebrating Nawrooz, killing dozens of people, many of them teenagers.
At least nine killed in Kabul suicide attack
IS's local franchise in Afghanistan claimed responsibility for the assault in the heavily Shia neighbourhood -- the fifth suicide bombing in the Afghan capital in recent weeks -- via the messaging app Telegram.
The blast killed 33 and wounded 65, the health ministry said, up from an earlier toll given by the interior ministry of 26 dead and 18 hurt.
All the injured were civilians, said interior ministry spokesperson Nasrat Rahimi.
Despite calls for the Taliban to sit down with the Afghan government, the group -- which has been resurgent since the withdrawal of US-led NATO combat troops at the end of 2014 -- appears to have few reasons to negotiate.
In October, insurgents controlled or influenced nearly half of Afghanistan's districts -- double the percentage in 2015, the US government's office of the Special Inspector General for Afghanistan Reconstruction said in January.
Over the same period, the watchdog said, the number of districts under Afghan government control or influence fell to its lowest level since December 2015.
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