With frequent flaring activity of its relativistic jets, Cygnus X‐3 (Cyg X‐3) is one of the most active microquasars and is the only Galactic black hole candidate with confirmed high‐energy γ‐ray emission, thanks to detections by Fermi Large Area Telescope (Fermi/LAT) and AGILE. In 2011, Cyg X‐3 was observed to transit to a soft X‐ray state, which is known to be associated with high‐energy γ‐ray emission. We present the results of a multiwavelength campaign covering a quenched state, when radio emission from Cyg X‐3 is at its weakest and the X‐ray spectrum is very soft. A giant (∼20 Jy) optically thin radio flare marks the end of the quenched state, accompanied by rising non‐thermal hard X‐rays. Fermi/LAT observations (E≥ 100 MeV) reveal renewed γ‐ray activity associated with this giant radio flare, suggesting a common origin for all non‐thermal components. In addition, current observations unambiguously show that the γ‐ray emission is not exclusively related to the rare giant radio flares. A three‐week period of γ‐ray emission is also detected when Cyg X‐3 was weakly flaring in radio, right before transition to the radio quenched state. No γ‐rays are observed during the ∼1‐month long quenched state, when the radio flux is weakest. Our results suggest transitions into and out of the ultrasoft X‐ray (radio‐quenched) state trigger γ‐ray emission, implying a connection to the accretion process, and also that the γ‐ray activity is related to the level of radio flux (and possibly shock formation), strengthening the connection to the relativistic jets.