The other employee, a Chadian national, was released just days after an armed attack, which took place in the Ade region close to the border with Sudan.
In March, British charity Oxfam estimated that 25 attacks occur every month on non-governmental organisations operating in eastern Chad.
The violence is often blamed on bandits, and NGOs have frequently denounced the lack of adequate security.
In August, General Daggache had threatened to expel MSF from Chad's volatile east if the organisation did not beef up its security.
The region is home to hundreds of thousands of refugees from Sudan's war-wracked Darfur, where fighting was declared officially over just recently, and from nearby Central African Republic.
There are an estimated 450,000 refugees and displaced people in the arid area, putting a great strain on food resources and firewood.
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