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We report on the demonstration of low-loss, single-mode GaN-InAlN ridge waveguides (WGs) at fiber-optics telecommunication wavelengths. The structure grown by metal-organic vapor phase epitaxy contains AlInN cladding layers lattice-matched to GaN. For slab-like WGs propagation losses are below 3 dB/mm and independent of light polarization. For 2.6-mum-wide WGs the propagation losses in the 1.5- to 1.58-mum spectral region are as low as 1.8 and 4.9 dB/mm for transverse-electric- and transverse-magnetic-polarization, respectively. The losses are attributed to the sidewall roughness and can be further reduced by the optimization of the etching process.