A doctor at the hospital in Farah said many of the wounded were children.
"A suicide bomber riding a motorcycle carried out the attack in the centre of Farah town in the area of Ada Herat," Faqir Ahmad Askar, a police official, told the AFP news agency.
The attack comes a day after Afghan President Hamid Karzai was sworn in for a second term as the country's elected leader.
David Chater, Al Jazeera's correspondent in Kabul, said: "This attack comes on the back of two other suicide bombing attacks on inauguration day.
"It's a reminder that after the euphoria and hopes surrounding the inauguration address by president Karzai, day two of his second term in office we are seeing the death toll mount rapidly yet again.
"Last month, October was the deadliest month for the American forces since the invasion began in 2001 and the same accounts for the civilians as well - they are the people who are suffering most at the moment."
Farah, a mainly desert province along the border with Iran, is one of the areas that has seen a rise in attacks this year as Taliban fighters have spread to the west and north from their traditional bases in the south and east.