Changing rates of water input can affect both the flow of glaciers and ice sheets and their propensity to crevasse. Here we examine geodetic and seismic observations during two substantial (10–18-times background velocity) rain-induced glacier accelerations at Haupapa/Tasman Glacier, New Zealand. Changes in rain rate result in glacier acceleration and associated uplift, which propagate down-glacier. This pattern of acceleration results in a change to the strain rate field, which correlates with an order of magnitude increase in the apparent seismicity rate and an overall down-glacier migration in located seismicity. After each acceleration event the apparent seismicity rate decreases to below the pre-acceleration rate for 3 days. This suggests that seismic events associated with surface crevasse growth occur early during phases of glacier acceleration due to elevated extensional stresses, and then do not occur again until stresses recover.