The Padres placed Miller on the postseason paternity list Tuesday, Alden Gonzalez of ESPN.com reports.
Miller will be permitted to spend no more than three days away from the team while he welcomes a new addition to his family, and he'll be allowed to rejoin the active roster immediately upon returning if San Diego is able to extend the series. In the meantime, the Padres will add Wandy Peralta to their NLDS roster to replace Miller in the bullpen.