The existence of fractionally charged particles (FCP) is foreseen in extensions of or beyond the Standard Model of particle physics. Most of the previously conducted searches for FCPs in cosmic rays were based on experiments underground or at high altitudes. However, there have been few searches for FCPs in cosmic rays carried out in orbit other than AMS-01 flown by a space shuttle and BESS by a balloon at the top of the atmosphere. In this study, we conduct an FCP search in space based on on-orbit data obtained using the Dark Matter Particle Explorer (DAMPE) satellite over a period of five years. Unlike underground experiments, which require an FCP energy of the order of hundreds of GeV, our FCP search starts at only a few GeV. An upper limit of $6.2\times 10^{-10}~~\mathrm{cm^{-2}sr^{-1} s^{-1}}$ is obtained for the flux. Our results demonstrate that DAMPE exhibits higher sensitivity than experiments of similar types by three orders of magnitude that more stringently restricts the conditions for the existence of FCP in primary cosmic rays.