Density estimation for marine mammal species is performed primarily using visual distance sampling or capture-recapture. Minke whales in Hawaiian waters are very difficult to sight; however, they produce a distinctive “boing” call, making them ideal candidates for passive acoustic density estimation. We used an array of 14 bottom-mounted hydrophones, distributed over a 60 × 30 km area off Kauai, Hawaii, to estimate density during 12 d of recordings in early 2006. We converted the number of acoustic cues (i.e., boings) detected using signal processing software into a cue density by accounting for the false positive rate and probability of detection. The former was estimated by manual validation, the latter by applying spatially explicit capture-recapture (SECR) methods to a subset of data where we had determined which hydrophones detected each call. Estimated boing density was 130 boings per hour per 10,000 km2 (95% CI 104–163). Little is known about the population's acoustic behavior, so conversion from boing to animal density is difficult. As a demonstration of the method, we used a tentative boing rate of 6.04 boings per hour, from a single animal tracked in 2009, to give an estimate of 21.5 boing-calling minke whales per 10,000 km2.