Reliable doping is required to realize many devices based on semiconductor nanowires. Group IIIV nanowires show great promise as elements of high-speed optoelectronic devices, but for such applications it is important that the electron mobility is not compromised by the inclusion of dopants. Here we show that GaAs nanowires can be n-type doped with negligible loss of electron mobility. Molecular beam epitaxy was used to fabricate modulation-doped GaAs nanowires with Al0.33Ga0.67As shells that contained a layer of Si dopants. We identify the presence of the doped layer from a high-angle annular dark field scanning electron microscopy cross-section image. The doping density, carrier mobility, and charge carrier lifetimes of these n-type nanowires and nominally undoped reference samples were determined using the noncontact method of optical pump terahertz probe spectroscopy. An n-type extrinsic carrier concentration of 1.10 +/- 0.06 x 10(16) cm(3) was extracted, demonstrating the effectiveness of modulation doping in GaAs nanowires. The room-temperature electron mobility was also found to be high at 2200 +/- 300 cm(2) V-1 s(-1) and importantly minimal degradation was observed compared with undoped reference nanowires at similar electron densities. In addition, modulation doping significantly enhanced the room-temperature photoconductivity and photoluminescence lifetimes to 3.9 +/- 0.3 and 2.4 +/- 0.1 ns respectively, revealing that modulation doping can passivate interfacial trap states.