  We study Shimura curves of PEL type in $\mathsf{A}_g$ generically contained
in the Prym locus. We study both the unramified Prym locus, obtained using
\'etale double covers, and the ramified Prym locus, corresponding to double
covers ramified at two points. In both cases we consider the family of all
double covers compatible with a fixed group action on the base curve. We
restrict to the case where the family is 1-dimensional and the quotient of the
base curve by the group is $\mathbb{P}^1$. We give a simple criterion for the
image of these families under the Prym map to be a Shimura curve. Using
computer algebra we check all the examples gotten in this way up to genus 28.
We obtain 43 Shimura curves generically contained in the unramified Prym locus
and 9 families generically contained in the ramified Prym locus. Most of these
curves are not generically contained in the Jacobian locus.
