The severity of recent declines of barren‐ground caribou (Rangifer tarandus groenlandicus) across the central Canadian Arctic has led to harvest restrictions and concerns about population recovery. Wolves (Canis lupus) are the main predator of barren‐ground caribou; however, the extent that wolves influence the decline and recovery of caribou herds is unknown. Such uncertainty confounds management responses (e.g., reducing harvest, predator control). We investigated wolf–caribou dynamics on the summer range of barren‐ground caribou in the Northwest Territories and Nunavut, Canada (i.e., Bathurst caribou herd). Our primary objective was to test for a numerical response of wolves to changes in the abundance and spatial distribution of caribou. Caribou experienced a >90% decline in abundance over the study period (1996–2014). Using long‐term data sets (1996–2012), we developed regression models to investigate relationships between abundance indices of wolves and range‐use patterns of caribou. We monitored the movements of adult female wolves fitted with global positioning system (GPS) collars representing individual packs throughout the 2013 and 2014 denning periods. We also investigated pup recruitment, an index of population decline, at a time of low caribou abundance. Finally, we developed a series of stochastic population models to understand how pup recruitment influenced wolf densities on the Bathurst range over the period of caribou decline. As caribou abundance decreased, the late‐summer distribution of the Bathurst herd contracted toward the calving ground. These movements correlated with low rates of wolf pup recruitment and high den abandonment, suggesting a regulatory mechanism whereby wolf reproductive success was limited by the low availability of caribou within the denning areas. Furthermore, these data suggested a numerical response, where wolf densities decreased as caribou numbers declined. In 2014, wolf density was estimated at <4 wolves/1,000 km2. Our results suggest that these wolves exhibited a relatively strong numerical response to a single, declining prey base. Given the continued decline in the Bathurst caribou herd, the tundra wolf population on the Bathurst range has likely declined below our 2014 estimate. © 2016 The Wildlife Society.