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We present a comprehensive noise model for vertical-cavity surface-emitting lasers (VCSELs). The time-domain model accounts for the stochastic fluctuations in the local carrier density in the separate confinement heterostructure and quantum wells, and in the modal intensity and phase of both the internal and the out-coupled optical field. In this work, we consider these fluctuations to be caused by the temporal uncertainty of the processes that supply or consume carriers and photons, such as carrier diffusion and photons escaping the cavity, and the processes that create or annihilate carriers and photons, such as stimulated emission and absorption. The noise model is based on a deterministic quasithree-dimensional dynamic model that treats the carrier transport, heat generation and dissipation, and optical fields in the device. Langevin noise terms are derived and added to the rate equations in the numerical solution. The noise model is applied to simulate the noise characteristics of fundamental-mode stabilized VCSELs with a shallow, mode discriminating, surface relief. The relative intensity noise and frequency noise of the output are calculated. From the latter, the linewidth of the VCSEL can be estimated. The results are compared with those of conventional multimode VCSELs.