We report results from a one‐week multiwavelength campaign to monitor the BL Lacertae object (BL Lac) S5 0716+714 (on 2009 December 9–16). Nine ground‐based telescopes at widely separated longitudes and one space‐based telescope aboard the Swift satellite collected optical data. Radio data were obtained from the Effelsberg and Urumqi observatories and X‐ray data from Swift. In the radio bands, the source shows rapid [∼(0.5–1.5) d] intraday variability with peak amplitudes of up to ∼10 per cent. The variability at 2.8 cm leads by about 1 d the variability at 6 and 11 cm. This time lag and more rapid variations suggest an intrinsic contribution to the source's intraday variability at 2.8 cm, while at 6 and 11 cm, interstellar scintillation (ISS) seems to predominate. Large and quasi‐sinusoidal variations of ∼0.8 mag were detected in the V, R and I bands. The X‐ray data (0.2–10 keV) do not reveal significant variability on a 4 d time‐scale, favouring reprocessed inverse Compton over synchrotron radiation in this band. The characteristic variability time‐scales in radio and optical bands are similar. A quasi‐periodic variation of 0.9–1.1 d in the optical data may be present, but if so it is marginal and limited to 2.2 cycles. Cross‐correlations between radio and optical bands are discussed. The lack of a strong radio–optical correlation indicates different physical causes of variability (ISS at long radio wavelengths, source intrinsic origin in the optical) and is consistent with a high jet opacity and a compact synchrotron component peaking at ≃100 GHz in an ongoing very prominent flux‐density outburst. For the campaign period, we construct a quasi‐simultaneous spectral energy distribution, including γ‐ray data from the Fermi satellite. We obtain lower limits for the relativistic Doppler boosting of δ ≥ 12–26, which for a BL Lac‐type object is remarkably high.