Mandatory or voluntary reductions in ship speed are a common management strategy for reducing deleterious encounters between large ships and large whales. This has produced strong resistance from shipping and marine transportation entities, in part because very few studies have empirically demonstrated whether or to what degree ship speed influences ship-whale encounters. Here we present the results of four years of humpback whale sightings made by observers aboard cruise ships in Alaska, representing 380 cruises and 891 ship-whale encounters. Encounters occurred at distances from 21 m to 1000 m (x = 567 m) with 61 encounters (7%) occurring between 200 m and 100 m, and 19 encounters (2%) within 100 m. Encounters were spatially aggregated and highly variable across all ship speeds. Nevertheless a Bayesian change-point model found that the relationship between whale distance and ship speed changed at 11.8 knots (6.1 m/s) with whales encountering ships, on average, 114 m closer when ship speeds were above 11.8 knots. Binning encounter distances by 1-knot speed increments revealed a clear decrease in encounter distance with increasing ship speed over the range of 7-17 knots (3.6-8.7 m/s). Our results are the first to demonstrate that speed influences the encounter distance between large ships and large whales. Assuming that the closer ships come to whales the more likely they are to be struck, our results suggest that reduced ship speed may be an effective management action in reducing the probability of a collision.