The discovery of γ-ray emission from radio-loud narrow-line Seyfert 1 (NLSy1) galaxies has questioned the need for large black hole masses ( ≳ 108 M⊙) to launch relativistic jets. We present near-infrared data of the γ-ray-emitting NLSy1 FBQS J1644+2619 that were collected using the camera CIRCE (Canarias InfraRed Camera Experiment) at the 10.4-m Gran Telescopio Canarias to investigate the structural properties of its host galaxy and to infer the black hole mass. The 2D surface brightness profile is modelled by the combination of a nuclear and a bulge component with a Sérsic profile with index n = 3.7, indicative of an elliptical galaxy. The structural parameters of the host are consistent with the correlations of effective radius and surface brightness against absolute magnitude measured for elliptical galaxies. From the bulge luminosity, we estimated a black hole mass of (2.1 ± 0.2) × 108 M⊙, consistent with the values characterizing radio-loud active galactic nuclei.