We report on the results of the low-frequency (1/f, where f is frequency) noise measurements in MoS2 field-effect transistors revealing the relative contributions of the MoS2 channel and Ti/Au contacts to the overall noise level. The investigation of the 1/f noise was performed for both as fabricated and aged transistors. It was established that the McWhorter model of the carrier number fluctuations describes well the 1/f noise in MoS2 transistors, in contrast to what is observed in graphene devices. The trap densities extracted from the 1/f noise data for MoS2 transistors, are 1.5 x 10^19 eV-1cm-3 and 2 x 10^20 eV-1cm-3 for the as fabricated and aged devices, respectively. It was found that the increase in the noise level of the aged MoS2 transistors is due to the channel rather than the contact degradation. The obtained results are important for the proposed electronic applications of MoS2 and other van der Waals materials.