Linear carbon-based materials such as polyyne and cumulene oligomers provide a versatile platform for nano-physics and engineering. Direct gap quasi-1D polyyne structures are promising for the observation of strong and unusual excitonic effects arising due to the two-dimensional quantum confinement. Recently, we reported on the observation of sharp exciton peaks in low temperature photoluminescence spectra of polyyne chains (Kutrovskaya S et al 2020 Nano Lett. 20 6502–9). Here, we analyze the time-resolved optical response of this system. We extend the non-local dielectric response theory to predict the exciton radiative lifetime dependence on the band-gap value and on the length of the chain. A good agreement between the experiment and the theory is achieved.