There was no immediately claim of responsibility, but similar incidents in the past have been blamed on Taliban fighters.
Police attacked
Also on Tuesday, at least nine policemen were killed in a battle with Taliban-linked fighters and bomb attacks in the southern Afghanistan province of Kandahar, a police commander said.
Five policemen were killed in an gunfight with Taliban-linked fighters who attacked their remote outpost in Shorabad, a district on the Afghan-Pakistani border, Sayed Agha Saqeb said.
Four other officers, who were despatched to the scene of the fighting as reinforcements, were killed when their vehicles were blown up by remote-controlled bombs, he said.
Bomb blasts usually target military convoys, but civilians are often killed instead.
According to a UN report, about 1,500 Afghan civilians have been killed in fighting in 2007.
Farah, which lies on the border with Iran, has seen a rise in attacks in recent months.
A soldier serving with the US-led coalition forces was killed in an operation there during the weekend.