There was no immediately claim of responsibility, but similar incidents in the past have been blamed on Taliban fighters.
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.