We consider dust production and entrainment into the atmosphere of Mars by impacts. Numerical simulations based on the multidimensional multimaterial hydrocode were conducted for impactors 1 to 100 m in size and velocities 11 and 20 km/s. The size distribution of particles was based on experiments using TNT explosions. Dust can be mobilized even when the impactor does not reach the ground through the release of energy in the atmosphere. We found that the blast-produced winds entrained dust by a mechanism similar to boundary layer winds as determined from the wind-tunnel tests. For a 1-m-radius stony asteroid releasing its energy in the atmosphere the lifted mass of dust is larger than that in a typical dust devil and could trigger local dust storms. For a 100-m-radius meteoroid the amount of injected dust is comparable with the total mass of a global dust storm.