The spectrum of any star viewed through a sufficient quantity of diffuse interstellar material reveals a number of absorption features collectively called `diffuse interstellar bands' (DIBs). The first DIBs were reported about 90years ago, and currently well over 500 are known. None of them has been convincingly identified with any specific element or molecule, although recent studies suggest that the DIB carriers are polyatomic molecules containing carbon. Most of the DIBs currently known are at visible and very near-infrared wavelengths, with only two previously known at wavelengths beyond one micrometre (10,000 ångströms), the longer of which is at 1.318micrometres (ref. 6). Here we report 13 diffuse interstellar bands in the 1.5-1.8 micrometre interval on high-extinction sightlines towards stars in the Galactic Centre. We argue that they originate almost entirely in the Galactic Centre region, a considerably warmer and harsher environment than where DIBs have been observed previously. The relative strengths of these DIBs towards the Galactic Centre and the Cygnus OB2 diffuse cloud are consistent with their strengths scaling mainly with the extinction by diffuse material.