A facile one-step Cu(I)-catalyzed “click” reaction, between a dansyl-azide and a propargyl-substituted rhodamine B hydrazide, is employed to fabricate a novel FRET ratiometric “off–on” fluorescent probe. The sensitive emission of the donor, a dansyl group, overlaps perfectly with the absorption of the acceptor, xanthene in the open-ring rhodamine. The proposed probe shows high selectivity towards Cu2+. The ratio of emission intensities at 568 and 540 nm (I568/I540) exhibits a drastic 28-fold enhancement upon addition of Cu2+. The probe shows an excellent linear relationship between emission ratios and the concentrations of Cu2+ from 10 to 50 μM, with a detection limit (S/N = 3) of 0.12 μM. The preliminary cellular studies demonstrated that the probe is cell membrane permeable and could be applied for ratiometric fluorescence imaging of intracellular Cu2+ with almost no cytotoxicity. The ingenuity of the probe design is to construct a FRET donor–acceptor interconnector and a selective receptor simultaneously by “click” reaction. The strategy was verified to have great potential for developing novel FRET probes for Cu2+.