Grid cells in the medial entorhinal cortex exhibit ultra-slow (<0.001 Hz) dynamics unfolding over seconds to minutes, as recently reported. The behavioral role of these oscillations remains unclear, particularly whether they influence position estimation from proprioceptive cues during path integration. Slow oscillations were found only in head-fixed mice on a running wheel, deprived of sensory input. Because these slow oscillations appear regardless of movement, we hypothesize that these dynamics only emerge under such restricted conditions, but are masked by sensory-driven activity during foraging. To test this hypothesis, we built a computational grid-cell model that forms a localized “packet” of neural activity representing the current position of a simulated rodent-like animal during 2D spatial navigation. Small synaptic changes due to synaptic plasticity induced a slow cyclical drift of the grid cell activity packet, even in the absence of sensory input, resembling the oscillations reported in vivo. This drift impaired path integration by causing position estimation errors, while also reactivating neural sequences consistent with recent trajectories. Notably, the slow oscillatory component was strongest when movement was constrained to one direction but was largely masked under unconstrained navigation. These results suggest that ultraslow entorhinal-like oscillations negatively affect path integration by increasing error in position estimation.