They were arrested by forces loyal to leader Moamer Kadhafi, their driver said.
The three journalists had not been heard from since March 18, 2011.
Driver Mohammed Hamed told AFP that on Saturday morning he took the three journalists from Tobruk on the road to Ajdabiya, where Kadhafi loyalists have been fighting eastern rebels.
A few dozen kilometres from Ajdabiya, they encountered a convoy of military jeeps and transport vehicles. They turned around, but were intercepted by the soldiers who caught up with them and forcibly arrested them, the driver said.
Four soldiers ordered the journalists out of their vehicle at gunpoint. Clark, an experienced foreign correspondent, identified themselves in Arabic as journalists, the driver said.
They were then ordered to kneel on the side of the road with their hands on their heads.
Other civilians and ambulances arrived on the scene and were controlled by soldiers who arrived in large number, Hamed said.
The soldiers then set fire to several vehicles, including that used by the journalists, who were put into a military vehicle and driven away.
Clark, 38, and Schmidt, 45, had informed AFP editors in an email on Friday of their plans to head 35 kilometres (22 miles) out of Tobruk.
They planned on meeting opponents of the regime of Libyan leader Moamer Kadhafi and speaking with refugees fleeing the battles between rebels and the loyalists.
Clark and Schmidt were accompanied by Raedle, 45, a photographer from the Getty Images agency.
The journalists had not been heard of since sending the email Friday night.
Paris-based Clark has been in Libya since March 8 while Schmidt, who normally works out of the Nairobi bureau, arrived in Libya on February 28.
Since the February 15 start of the insurrection against Kadhafi's regime, a number of foreign journalists have been arrested in Libya.
Four New York Times reporters, who were detained last week during the fighting between government and rebel forces, left the country safely on Monday after Turkey helped secure their release, the newspaper said.
On Saturday the Qatar-based Al-Jazeera satellite television said that four of its journalists, including a Norwegian and a Briton, are being held in Tripoli after being arrested in Libya's west.
Al-Jazeera cameraman Ali Hassan al-Jaber was killed on March 12 in an ambush near the rebel stronghold of Benghazi -- the first reported death by a foreign media of a journalist in Libya since the start of the uprising.
Mohammed al-Nabbous, 28, who founded a Libyan online news channel was shot dead by snipers in Saturday while Benghazi was under attack from Kadhafi's forces.