A Taliban spokesman told Al Jazeera's correspondent in Islamabad that the group only attacks foreign soldiers and those he described as their agents in the Afghan military.
Agencies said the target was a car carrying the province's police chief.
"Two civilians were killed and 33 were wounded... Three are in critical condition," the media office of the interior ministry in Kabul said.
The wounded included two of the police chief's bodyguards and the children. The rest were workers.
The bomb is believed to have been hidden in a rubbish skip.
Farah province has seen a surge in unrest in recent weeks blamed on opium traders or Taliban fighters, who captured the town of Bakwa for less than 24 hours last month before being forced out by Nato-led Afghan troops.
Meanwhile, in the violence-torn neighbouring province of Helmand, the bullet-riddled body of an Afghan doctor was found dumped near the remote area of Garmser which has seen much Taliban-related activity.
The doctor, who worked at a hospital in the provincial capital Lashkar Gah, had been missing since Saturday, Isah Khan, provincial security chief, said.
It is not known who was responsible for the killing.
The Taliban have kidnapped and executed dozens of people working for the government or foreign groups, accusing some of being spies.