A characterization as stated in the title is given, where a dendroid is understood as hereditarily unicoherent and arc-wise connected metrizable continuum. It is proved that a dendroid X has uncountably many end- points, iff either X contains some Gehman dendroid or X contains an uncountable family of pairwise disjoint non-degenerate arcs. A dendroid X is called Gehman, if it contains a set of the form \(f(G_{\omega})\) as a dense subset, where f is continuous, one-to-one and satisfies some additional condition, but \(G_{\omega}\) is the standard zero-one tree (without end-points).