Filament-wound composite tubular structures are frequently used in transmission systems, pressure vessels, and sports equipment. In this study, the failure mechanism of composite tubes reinforced with different fibres under low-velocity impact (LVI) and the radial residual compression performance of the impacted composite tubes were investigated. Four fibres, including carbon fiber-T800, carbon fiber-T700, basalt fibre, and glass fibre, were used to fabricate the composite tubes by the winding process. The internal matrix/fibre interface of the composite tubes before the LVI and their failure mechanism after the LVI were investigated by scanning electric microscopy and X-ray micro-computed tomography, respectively. The results showed that the composite tubes mainly fractured through the delamination and fibre breakage damage under the impact of 15 J energy. Delamination and localized fibre breakage occur in the glass fibre-reinforced composite (GFRP) and basalt fibre-reinforced composite (BFRP) tubes when subjected to LVI. While fibre breakage damage occurs globally in the carbon fibre-reinforced composite (CFRP) tubes. The GFRP tube showed the best impact resistance among all the tubes investigated. The basalt fibre-reinforced composite (BFRP) tube exhibited the lowest structural impact resistance. The impact resistance of the CFRP-T700 and CFRP-T800 tube differed slightly. The radial residual compression strength (R-RCS) of the BFRP tube is not sensitive to the impact, while that of the GFRP tube is shown to be highly sensitive to the impact.