Characteristics of GaAs/AlGaAs quantum wire (QWR) lasers are studied for the first time under strong magnetic fields up to 12T. The QWR laser diodes have been fabricated by the molecular beam epitaxy technique, we call “cleaved edge overgrowth” (CEO), which combines conventional layer growth along the [001] crystal axis with high-quality regrowth on the (110) crystal face formed by an in situ cleave. The active region of our lasers consists of atomically precise QWRs that form at the T-shaped intersections of 7 nm wide GaAs quantum wells (QWs). The origin of the quantum mechanical bound state is the relaxation of quantum well confinement at this intersection, which limits free carrier motion to one-dimension, i.e. to the line defined by the intersection of the two QWs. Applying a magnetic field parallel to the QWR axis we observe a pronounced increase in the laser emission intensity of more than one order of magnitude while the electrical diode characteristic remains unaffected. This effect mainly occurs for field strengths of 5 to 9 T where the magnetic length becomes comparable to the QWR dimensions. For a magnetic field direction oriented perpendicular to the QWR axis and parallel to the [110] overgrowth direction, a completely different behavior is observed. Although the absolute intensity increase is comparable to the previous case, the emitted intensity is already doubled for a magnetic field below 1 T, and magnetic fields exceeding 4 T show only a weak effect on the emitted intensity for this field direction. The origin of such a strong magnetic field dependence of the QWR emission, not previously observed for QW lasers, is discussed in the context of excitonic lasing.