We report on rapid, all-electronically controlled wavelength tuning of a continuous-wave (cw) optical parametric oscillator (OPO) pumped by an ytterbium fiber laser. The OPO is singly resonant for the signal wave and consists of a 40-mm-long periodically poled lithium niobate crystal in a four-mirror ring cavity. By tuning of the fiber-laser wavelength over 33 nm through an intracavity acousto-optic tunable filter, the OPO idler wavelength is tuned from 3160 to 3500 nm in 330 micros, corresponding to an idler frequency-tuning speed of 28 THz/ms. At a fiber-laser power of 6.6 W at 1074 nm, the singly resonant OPO generates 1.13-W cw idler radiation at 3200 nm.