<p>The unconventional behavior of quasiperiodic structures has become a focal point in condensed matter physics. This paper is devoted to the study of the Mode-I external circular crack lying in a one-dimensional hexagonal piezoelectric quasicrystal. The original problem is transformed into a mixed boundary value problem, which is solved by the generalized potential theory method. The exact full-field fundamental solutions of the problem are obtained in terms of elementary functions. For both electrically impermeable and permeable boundary conditions, important parameters in fracture mechanics are obtained in response to generalized concentrated loads and annular uniformly distributed loads. From the generalized stress intensity factors, a phonon/phason-electric coupling parameter is proposed to quantify the multiphysical interactions. The influence of the phonon-phason-electric coupling effect on the generalized crack surface displacement is characterized. The present study provides a basis for fracture behaviors of piezoelectric quasicrystals.</p>