An engine-driven work machine is provided in which an engine/work machine unit (5) and an exhaust muffler (23) are housed in a box (30), the box (30) is provided with a cooling air passage (44) that passes the area around the engine/work machine unit (5) and the exhaust muffler (23), and a cooling fan (15) driven by the engine (2) is disposed in the cooling air passage (44), wherein the box (30) is provided with blocking means (51) for blocking the cooling air passage (44) between the engine (2) and the exhaust muffler (23) when running of the engine (2) is stopped. The heat of the high temperature exhaust muffler can thus be prevented from affecting the engine/work machine unit even when running of the engine is stopped, while maintaining the soundproofing of the box housing the unit, etc.