The effects of AlGaAs shell thickness and growth time on the minority carrier lifetime in the GaAs core of GaAs/AlGaAs core-shell nanowires grown by metal-organic chemical vapor deposition are investigated. The carrier lifetime increases with increasing AlGaAs shell thickness up to a certain value as a result of reducing tunneling probability of carriers through the AlGaAs shell, beyond which the carrier lifetime reduces due to the diffusion of Ga-Al and/or impurities across the GaAs/AlGaAs heterointerface. Interdiffusion at the heterointerface is observed directly using high-angle annular dark field scanning transmission electron microscopy. We achieve room temperature minority carrier lifetimes of 1.9 ns by optimizing the shell growth with the intention of reducing the effect of interdiffusion.