The process of isothermal and non-isothermal physical ageing of amorphous polylactide (PLA) with the active pharmaceutical ingredient, indapamide (IND), was investigated. A PLA–IND system with a 50/50 weight ratio was obtained and characterized using differential scanning calorimetry (DSC). In the 50/50 (w/w) mixture, two glass transitions were observed: the first at 64.1 ± 0.3 °C corresponding to the glass transition temperature (Tg) of PLA, and the second at 102.6 ± 1.1 °C corresponding to the Tg of IND, indicating a lack of molecular mixing between the two ingredients. The PLA–IND system was subjected to the isothermal physical ageing process at different ageing temperatures (Ta) for 2 h. It was observed that the highest effect of physical ageing (enthalpy relaxation change) on IND in the PLA–IND system occurred at Ta = 85 °C. Furthermore, the system was annealed for various ageing times at 85 °C. The relaxation enthalpies were estimated for each experiment and fitted to the Kohlrausch–Williams–Watts (KWW) equation. The KWW equation allowed for the estimation of the relaxation time and the parameter describing the distribution of relaxation times of the isothermal physical ageing process of IND in the PLA–IND system. The physical ageing of the PLA–IND mixture (50/50) was also discussed in the context of heat capacity. Moreover, the activation energy and fragility parameters were determined for the PLA–IND (50/50) system.