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In this paper, we discuss the role of an external magnetic field on the dynamically generated fermion mass in even-flavor QED in three space-time dimensions. Based on some reasonable approximations, we present analytic arguments on the fact that, for weak fields, the magnetically-induced mass increases quadratically with increasing field, while at strong fields one crosses over to a mass scaling logarithmically with the external field. We also confirm this type of scaling behavior through quenched lattice calculations using the non-compact version for the gauge field. Both the zero and finite temperature cases are examined. A preliminary study of the fermion condensate in the presence of magnetic flux tubes on the lattice is also included.