Clark, a 38-year-old reporter, and photographer Schmidt, 45, had informed the agency 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 Muammar Gaddafi and speaking with refugees fleeing the battles between rebels and the loyalists.
Clark and Schmidt were accompanied by a photographer from the Getty Images agency, Joe Raedle. The three journalists have not been heard of since sending the email Friday night.
Paris-based Clark has been in Libya since Mar 8 while Schmidt, who normally works out of the Nairobi bureau, arrived in Libya on Feb 28.
Since the Feb 15 start of the insurrection against Gaddafi's regime, a number of foreign journalists have been arrested in Libya.
The authorities in Tripoli said they are holding four New York Times journalists after they went missing in the east of the country last Tuesday.
The paper said they were to be freed on Friday but there has been no confirmation that they were indeed released.
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.