Self-mode-locking has become an emerging path to the generation of ultrashort pulses with vertical-external-cavity surface-emitting lasers. In our work, a strong Kerr nonlinearity that is so far assumed to give rise to mode-locked operation is evidenced and a strong nonlinearity enhancement by the microcavity is revealed. We present wavelength-dependent measurements of the nonlinear absorption and nonlinear refractive index change in a gain chip using the Z-scan technique. We report negative nonlinear refraction up to 5x10-12 cm2/W in magnitude in the (InGa)As/Ga(AsP) material system close to the laser design wavelength, which can lead to Kerr lensing. We show that by changing the angle of incidence of the probe beam with respect to the gain chip, the Kerr nonlinearity can be wavelength-tuned, shifting with the microcavity resonance. Such findings may ultimately lead to novel concepts with regard to tailored self-mode-locking behavior achievable by peculiar Kerr-lens chip designs for cost-effective, robust and compact fs-pulsed semiconductor lasers.