Context: Near-Earth asteroid 162173 (1999 JU3) is the primary target of the Japanese Aerospace Exploration Agency (JAXA) Hayabusa-2 sample return mission, and is also on the list of potential targets for the European Space Agency (ESA) Marco Polo sample return mission. Earth-based studies of this object are fundamental to these missions. Aims: Our aim is to provide new constraints on the surface properties of this asteroid. Methods: We present a mid-infrared spectrum (5-38 μm) obtained with NASA's Spitzer Space Telescope in May 2008 and results from the application of thermal models. Results: These observations place new constraints on the surface properties of this asteroid. To fit our spectrum we used the near-Earth asteroid thermal model (NEATM) and the more complex thermophysical model (TPM). However, the position of the spin-pole, which is uncertain, is a crucial input parameter for constraining the thermal inertia with the TPM; hence, we consider two pole orientations. First is the extreme case of an equatorial retrograde geometry from which we derive a rigorous lower limit to the thermal inertia of 150 Jm-2 s-0.5 K-1. Second, when we adopt the pole orientation of Abe et al. (2008a, 37th COSPAR Scientific Assembly) our best-fit thermal model yields a value for the thermal inertia of 700 ± 200 Jm-2 s-0.5 K-1 and even higher values are allowed by the uncertainty in the spectral shape due to the absolute flux calibration. Our best estimates of the diameter (0.90 ± 0.14 km) and geometric albedo (0.07 ± 0.01) of asteroid 162173 are consistent with values based on previous mid-infrared observations. Conclusions: We establish a rigorous lower limit to the thermal inertia, which is unlikely but possible, and would be consistent with a fine regolith similar to wthat is found for asteroid 433 Eros. However, the thermal inertia is expected to be higher, possibly similar to or greater than that on asteroid 25143 Itokawa. An Accurately determining the spin-pole of asteroid 162173 will narrow the range of possible values for its thermal inertia.