In September 2016, the microquasar Cygnus X-3 underwent a giant radio flare, which was monitored for 6 days with the Medicina Radio Astronomical Station and the Sardinia Radio Telescope. Long observations were performed in order to follow the evolution of the flare on a hourly scale, covering six frequency ranges from 1.5 GHz to 25.6 GHz. The radio emission reached a maximum of 13.2 ± 0.7 Jy at 7.2 GHz and 10 ± 1 Jy at 18.6 GHz. Rapid flux variations were observed at high radio frequencies at the peak of the flare, together with rapid evolution of the spectral index: α steepened from 0.3 to 0.6 (with S ν ∝ ν −α ) within 5 hours. This is the first time that such fast variations are observed, giving support to the evolution from optically thick to optically thin plasmons in expansion moving outward from the core. Based on the Italian network (Noto, Medicina and SRT) and extended to the European antennas (Torun, Yebes, Onsala), VLBI observations were triggered at 22 GHz on five different occasions, four times prior to the giant flare, and once during its decay phase. Flux variations of 2-hour duration were recorded during the first session. They correspond to a mini-flare that occurred close to the core ten days before the onset of the giant flare. From the latest VLBI observation we infer that four days after the flare peak the jet emission was extended over 30 mas.