Ethylene-based copolymer microparticles and functional group-containing ethylene-based copolymer microparticles that have particle diameter smaller than that of conventional polyethylene fine-particles, no inter-particle agglomeration, very narrow particle size distribution, and high sphericity are provided, in which requirements (A) to (E): (A) The intrinsic viscosity [.eta.] measured in decalin at 135.degree. C. is in the range of 0.1 to 50 dl/g, (B) at least 95 wt % or more of particles pass through a mesh screen with an opening of 37 .mu.m, (C) the median diameter (d.sub.50) measured by laser diffraction scattering is 3 .mu.m.ltoreq.d.sub.50.ltoreq.25 .mu.m, (D) the circularity coefficient is 0.85 or more, and (E) the variation coefficient of particle diameter (Cv) is 20% or less. Non-agglomerated spherical magnesium-containing microparticles used as magnesium-containing carrier component for olefin-polymerization catalysts that can manufacture the above microparticles are also provided.