Simultaneous multi-slice (multiband) acceleration in fMRI has become widespread, but may be affected by novel forms of signal artifact. Here, we demonstrate a previously unreported artifact manifesting as a shared signal between simultaneously acquired slices in all resting-state and task-based multiband fMRI datasets we investigated, including publicly available consortium data from the Human Connectome Project (HCP) and Adolescent Brain Cognitive Development (ABCD) Study. We propose Multiband Artifact Regression in Simultaneous Slices (MARSS), a regression-based detection and correction technique that successfully mitigates this shared signal in unprocessed data. We demonstrate that the signal isolated by MARSS correction is likely nonneural, appearing stronger in neurovasculature than gray matter. Additionally, we evaluate MARSS both against and in tandem with sICA+FIX denoising, which is implemented in HCP resting-state data, to show that MARSS mitigates residual artifact signal that is not modeled by sICA+FIX. MARSS correction leads to study-wide increases in signal-to-noise ratio, decreases in cortical coefficient of variation, and mitigation of systematic artefactual spatial patterns in participant-level task betas. Finally, MARSS correction has substantive effects on second-level t-statistics in analyses of task-evoked activation. We recommend that investigators apply MARSS to multiband fMRI datasets with moderate or higher acceleration factors, in combination with established denoising methods.