The low modulation bandwidth of deep-ultraviolet (UV) light sources is considered as the main reason limiting the data transmission rate of deep-UV communications. Here, we present high-bandwidth III-nitride micro-light-emitting diodes (μLEDs) emitting in the UV-C region and their applications in deep-UV communication systems. The fabricated UV-C μLEDs with $566{\mathrm{\mu m}}^2$ emission area produce an optical power of 196 μW at the $3400\mathrm{A}/{\mathrm{cm}}^2$ current density. The measured 3 dB modulation bandwidth of these μLEDs initially increases linearly with the driving current density and then saturates as 438 MHz at a current density of $71\mathrm{A}/{\mathrm{cm}}^2$, which is limited by the cutoff frequency of the commercial avalanche photodiode used for the measurement. A deep-UV communication system is further demonstrated. By using the UV-C μLED, up to 800 Mbps and 1.1 Gbps data transmission rates at bit error ratio of $3.8\times {10}^3$ are achieved assuming on-off keying and orthogonal frequency-division multiplexing modulation schemes, respectively.