Low-frequency electrical current noise measurements are reported on double-heterojunction AlGaAs/GaAs laser diodes fabricated on GaAs and on Si substrates. The noise spectra show a frequency dependence proportional with f-γ with γ close to unity. The spectral intensity is proportional to the current for smaller currents (<0.1 mA) and levels off at larger currents (>1 mA). The diodes built on the GaAs substrate are 50 times less noisy than the ones built on the Si substrate. This effect is attributed to the fact that the density of dislocations at the Si interface is much larger than at the GaAs substrate/device interface.