We present a study of the polarization properties of emission lines from single InGaN/GaN quantum dots (QDs). The QDs, formed by spinodal decomposition within ultra-thin InGaN quantum wells, are investigated using single-QD cathodoluminescence (CL). The emission lines exhibit a systematic linear polarization in the orthogonal crystal directions [1 1 -2 0] and [-1 1 0 0]--a symmetry that is non-native to hexagonal crystals. Eight-band k.p calculations reveal a mechanism that can explain the observed polarizations: The character of the hole(s) in an excitonic complex determines the polarization direction of the respective emission if the QD is slightly elongated. Transitions involving A-band holes are polarized parallel to the elongation; transitions involving B-type holes are polarized in the orthogonal direction. The energetic separation of both hole states is smaller than 10 meV. The mechanism leading to the linear polarizations is not restricted to InGaN QDs, but should occur in other wurtzite-nitride QDs and in materials with similar valence band structure.