Context. Gravitational collapse theory and numerical simulations suggest that the velocity field within large-scale galaxy filaments is dominated by motions along the filaments. Aims. Our aim is to check whether observational data reveal any preferred orientation of galaxy pairs with respect to the underlying filaments as a result of the expectedly anisotropic velocity field. Methods. We use galaxy pairs and galaxy filaments identified from the Sloan Digital Sky Survey data. For filament extraction, we use the Bisous model that is based the marked point process technique. During the filament detection, we use the centre point of each pair instead of the positions of galaxies to avoid a built-in influence of pair orientation on the filament construction. For pairs lying within filaments (3012 cases), we calculate the angle between the line connecting galaxies of each pair and their host filament. To avoid redshift-space distortions, the angle is measured in the plain of the sky. Results. The alignment analysis shows that the orientation of galaxy pairs correlates strongly with their host filaments. The alignment signal is stronger for loose pairs, with at least 25% excess of aligned pairs compared to a random distribution. The alignment of galaxy pairs and filaments measured from the observational data is in good concordance with the alignment in the Millennium simulation and thus provides support to the {Lambda}CDM formalism.