Aims: We aim to study the near-infrared linear polarization signal of rapidly rotating ultracool dwarfs with spectral types ranging from M7 through T2 and projected rotational velocities of v sin i ≳ 30 km s-1. These dwarfs are believed to have dusty atmospheres and oblate shapes, which is an appropriate scenario to produce measurable linear polarization of the continuum light. Methods: Linear polarimetric images were collected in the J-band for a sample of 18 fast-rotating ultracool dwarfs, of which five were also observed in the Z-band using the Long-slit Intermediate Resolution Infrared Spectrograph (LIRIS) on the Cassegrain focus of the 4.2-m William Herschel Telescope. The measured median uncertainty in the linear polarization degree is ±0.13% for our sample, which allowed us to detect polarization signatures above ~0.39% with a confidence interval of ≥3σ. Results: About 40 ± 15% of the sample is linearly polarized in the Z- and J-bands. All positive detections have linear polarization degrees ranging from 0.4% to 0.8% in both filters independent of spectral type and spectroscopic rotational velocity. However, simple statistics point at the fastest rotators (v sin i ≳ 60 km s-1) having a larger fraction of positive detections and a larger averaged linear polarization degree than the moderately rotating dwarfs (v sin i = 30-60 km s-1). Our data suggest little linear polarimetric variability on short timescales (i.e., observations separated by a few ten rotation periods), and significant variability on long timescales (i.e., hundred to thousand rotation cycles), supporting the presence of long-term weather in ultracool dwarf atmospheres.