Context. The extreme teraelectronvolt (TeV) blazar 1ES 0229+200 is a high-frequency-peaked BL Lacertae object. It has not shown intraday variability in extensive optical and X-ray observations, nor has it shown any significant variability on any measurable timescale in the 1–100 GeV energy range over a 14-year span; however, variations in the source flux around its average are present in the energy range above 200 GeV. Aims. We aim to search for intraday optical variability in 1ES 0229+200 as part of an ongoing project to search for variability and quasi-periodic oscillations in the high-cadence (2 min), nearly uniformly sampled optical light curves of blazars provided by the Transiting Exoplanet Survey Satellite (TESS). Methods. 1ES 0229+200 was monitored by TESS in its Sectors 42, 43, and 44. We analysed the data of all these three sectors both with the TESS-provided lightkurve software and the eleanor reduction pipeline. We detected a strong, essentially symmetric flare that lasted about 6 h in Sector 42. We fitted the flare’s rising and declining phases to exponential functions. We also analysed the light curve of Sector 42 using the Lomb-Scargle periodogram (LSP) and continuous auto-regressive moving average (CARMA) methods. Results. The optical light curve of Sector 42 of the TESS observations displayed in the present work provides the first evidence of a strong, rapid, short-lived optical flare on the intraday timescale in the TeV blazar 1ES 0229+200. The variability timescale of the flare provides the upper limit for the size of the emission region to be within (3.3 ± 0.2–8.3 ± 0.5)×1015 cm. Away from the flare, the slope of the periodogram’s power spectrum is fairly typical of many blazars (α < 2), but the nominal slopes for the flaring regions are very steep (α ∼ 4.3), which may indicate that the electron distribution undergoes a sudden change. We discuss possible emission mechanisms that could explain this substantial and rapid flare.