Binary properties are an important diagnostic of the star and brown dwarf formation processes. While wide binaries appear to be rare in the sub-stellar regime, recent observations have revealed Ophiuchus 162225-240515 (2MASS J16222521-2405139) as a likely young ultra-low-mass binary with an apparent separation of ~240 AU. Here, we present low-resolution near-infrared spectra of the pair from NTT/SOFI (R~600) and VLT/ISAAC (R~1400), covering the 1.0-2.5um spectral region. By comparing to model atmospheres from Chabrier & Baraffe and Burrows et al., we confirm the surface temperatures to be T_A = (2350+/-150) K and T_B = (2100+/-100) K for the two components of the binary, consistent with earlier estimates from optical spectra. Using gravity sensitive K I features, we find the surface gravity to be significantly lower than field dwarfs of the same spectral type, providing the best evidence so far that these objects are indeed young. However, we find that models are not sufficiently reliable to infer accurate ages/masses from surface gravity. Instead, we derive masses of M_A = 13 (+8/-4) M_J and M_B = 10 (+5/-4) M_J for the two objects using the well-constrained temperatures and assuming an age of 1-10 Myr, consistent with the full range of ages reported for the Oph region.