Cometary outgassing can produce torques that change the spin state of the cometary nucleus, which in turn influences the evolution and lifetime of the comet(1,2). If these torques increase the rate of rotation to the extent that centripetal forces exceed the material strength of the nucleus, the comet can fragment(3). Torques that slow down the rotation can cause the spin state to become unstable, but if the torques persist the nucleus can eventually reorient itself and the rotation rate can increase again(4). Simulations predict that most comets go through a short phase of rapid changes in spin state, after which changes occur gradually over longer times(5). Here we report observations of comet 41P/Tuttle-Giacobini-Kresak during its close approach to Earth (0.142 astronomical units, approximately 21 million kilometres, on 1 April 2017) that reveal a rapid decrease in rotation rate. Between March and May 2017, the apparent rotation period of the nucleus increased from 20 hours to more than 46 hours-a rate of change of more than an order of magnitude larger than has hitherto been measured. This phenomenon must have been caused by the gas emission from the comet aligning in such a way that it produced an anomalously strong torque that slowed the spin rate of the nucleus. The behaviour of comet 41P/Tuttle-Giacobini-Kresak suggests that it is in a distinct evolutionary state and that its rotation may be approaching the point of instability.