An experimental investigation of the modal selection induced by optical injection in 1550 nm multitransverse-mode VCSELs is performed. The free-running VCSEL emits in two transverse modes that are linearly polarized in a direction referred as parallel. We consider the situation in which parallel polarized laser light is injected in the VCSEL in order to select its fundamental transverse mode. We analyze the dependence of the modal selection process on the wavelength detuning between the externally injected signal and the fundamental mode. The injected power needed to select the fundamental mode as a function of the wavelength detuning is measured for several values of the bias current. This injected power exhibits a minimum at a positive wavelength detuning. The curves obtained for different bias currents are very close for positive and large wavelength detuning, while they are very separated for smaller detuning. The selection of the fundamental mode can be obtained with a value of the injected power that changes only slightly with the bias current when the wavelength detuning is large and positive. These results indicate that operation at large and positive wavelength detuning is of interest in the long-distance single-mode fiber transmission of multimode injection-locked VCSELs because the selection of the fundamental mode is obtained with an injected power that is almost independent on the VCSEL bias current. Both, the minimum injected power and the wavelength detuning at which it appears increase with the VCSEL bias current. We describe the relation between transverse mode selection and injection locking by comparing the dependence of both phenomena on the wavelength detuning. Modal selection is accompanied by injection locking only for large and positive values of the wavelength detuning. For small detuning values, with the VCSEL biased with a low (high) current, the injected power required for modal selection is lower (higher) than that needed for injection locking.