Electrospun poly(lactic-co-glycolic acid) (PLGA) scaffolds with highly aligned fibers (ha-PLGA) represent promising materials in the field of tendon tissue engineering (TE) due to their characteristics in mimicking fibrous extracellular matrix (ECM) of tendon native tissue. Among these properties, scaffold biodegradability must be controlled allowing its replacement by a neo-formed native tendon tissue in a controlled manner. In this study, ha-PLGA were subjected to hydrolytic degradation up to 20 weeks, under di-H2O and PBS conditions according to ISO 10993-13:2010. These were then characterized for their physical, morphological, and mechanical features. In vitro cytotoxicity tests were conducted on ovine amniotic epithelial stem cells (oAECs), up to 7 days, to assess the effect of non-buffered and buffered PLGA by-products at different concentrations on cell viability and their stimuli on oAECs’ immunomodulatory properties. The ha-PLGA scaffolds degraded slowly as evidenced by a slight decrease in mass loss (14%) and average molecular weight (35%), with estimated degradation half-time of about 40 weeks under di-H2O. The ultrastructure morphology of the scaffolds showed no significant fiber degradation even after 20 weeks, but alteration of fiber alignment was already evident at week 1. Moreover, mechanical properties decreased throughout the degradation times under wet as well as dry PBS conditions. The influence of acid degradation media on oAECs was dose-dependent, with a considerable effect at 7 days’ culture point. This effect was notably reduced by using buffered media. To a certain level, cells were able to compensate the generated inflammation-like microenvironment by upregulating IL-10 gene expression and favoring an anti-inflammatory rather than pro-inflammatory response. These in vitro results are essential to better understand the degradation behavior of ha-PLGA in vivo and the effect of their degradation by-products on affecting cell performance. Indeed, buffering the degradation milieu could represent a promising strategy to balance scaffold degradation. These findings give good hope with reference to the in vivo condition characterized by physiological buffering systems.