Laser beam surface treatment of various materials is currently successfully used in various manufacturing processes. This paper presents the results of experimental studies and analyses of the effect of selected parameters of fiber laser treatment of the surface of an EN AW-5754 aluminum alloy. This alloy contains magnesium, chromium, and manganese and is used as a structural material in construction, railways, maritime transport, aviation, mechanical engineering, and other industries. A 1 mm thick sheet was used in the experiment, and the surface was treated with a fiber laser according to eight variants. The variants were differentiated by the number of treatment repetitions (10, 15, and 20 times), pulse frequency (25 and 45 kHz), and beam speed relative to the surface (100 and 200 mm/s). The residual stresses on samples with modified surfaces were measured using an X-ray diffractometer. The results were compared with stresses measured on sandblasted and rolled surfaces. It was found that, unlike with rolling and sandblasting, tensile stresses were formed after laser processing. Laser processing, which results in a relatively repeatable geometric surface structure, influenced the variation of these stress values depending on the directionality of the geometric structure. The results obtained in this way can be used during laser surface processing in cases where the surface structure created by the laser is important. Still, the appropriate direction of the forces acting on the structure must also be selected.