"When the prayers started at the main mosque of Lashkar Gah ... a suicide attacker who had strapped explosives to his body detonated," Andiwal said.
He added that a four-year-old child "who was sitting at the entrance of the mosque and was begging" was among those wounded in the attack.
Faqir Mohammad Askar, a second provincial police chief, said: "The enemy of Afghanistan is an enemy of religion ... With a suicide attack inside a mosque."
Zeina Khodr, Al Jazeera's correspondent in Afghanistan, said the Taliban claimed responsibility for the attack and that this was the first time a suicide attack had been carried out in a place of worship.
A spokesman for the Taliban, Zabihullah Mujahed, confirmed the attack was carried out by one of the group's men and said it was aimed at the deputy governor.
Hamid Karzai, Afghanistan's president, condemned the bombings as "Unislamic", adding that it showed the Taliban's weakness.
But the targeting of a mosque may in fact signal a change in the Taliban's tactics, Khodr said.
The bombing came soon after at least one person was killed by a suicide blast in Kabul, the Afghan capital.
Several more people were wounded in the Kabul explosion, which appeared to target an Afghan army bus.
The bus, which had been taking Afghan soldiers to work, was left burning in the street and ambulances were seen leaving the scene with their sirens on.
Zemarai Bashary, an interior ministry spokesman, said: "It was a suicide car bomb.
The target was apparently an ANA [Afghan National Army] vehicle." At least two people were wounded, including another person in a taxi and a man who had been riding a bicycle directly behind the car bomb, he said.
Zabihullah Mujahed, a Taliban spokesman, said that the group was responsible for the attack.
Mohammad Sharif, a witness, said: "I ran out. Police at the roundabout starting shooting in the air. I saw a man screaming, lying on the road with his bicycle."
Sharif also said that two taxis were damaged, estimating that three or four of the passengers were wounded.
The bombing in Kabul comes after an assault by Taliban fighters, on January 14, on Kabul's only five-star hotel.
The Taliban claimed responsibility for the attack in which at least eight people were killed.
In other violence in Afghanistan, in the east of the country, the decapitated bodies of four Afghan construction workers who went missing last week have also been found.
The attacks come in the wake of US report that warns Afghanistan could become a "failed state" if steps are not taken to tackle a deteriorating security situation.