The men, all Afghans, were employed by the HALO Trust, based in Dumfries.
Rauf Ahmadi, the spokesman for the police chief of the western Herat province, said a military operation has been launched in the area to free the workers.
He said six suspects had already been detained and the hunt was on to trace more of the suspected gunmen.
He said tribal elders from the local area had tried negotiating the workers’ release but did not give any further details.
Mr Ahmadi said all 11 of the staff were abducted on Friday.
A spokesman for the Thornhill-based HALO Trust said: “We can confirm there was a security incident in Afghanistan.
“We are working with the Afghan authority to secure their safe release.”
Abductions are widespread in Afghanistan, with many people kidnapped for ransom.
People employed as mine clearers are seen as “soft targets” as they usually work in more remote regions.
After almost 40 years of war, Afghanistan is one of the most heavily mined countries in the world.
The HALO Trust says there have been up to 640,000 land mines laid in the country since 1979.
More than three decades of war has left the country littered with unexploded mines.As a result, there were more than 23,500 casualties recorded between 1979 and 2015.
The Trust began working in the country in 1988 and currently employs 2,400 Afghans.
The HALO Trust was founded in 1988 in response to the global humanitarian catastrophe caused by landmines.
The problem was particularly acute in Afghanistan where thousands of civilians were being killed or injured by landmines and their presence was preventing the return of tens of thousands of refugees.