Recently, environmentally degradable polymers have received great attention from the perspective of sustaining the aquatic environment. To control the degradation behavior of solid polymer materials in an aqueous phase, it is crucial to better understand the thermal molecular motion of polymer chains in water. We herein focus on polyglycolide (PGA), which is one of the representative aliphatic polyesters that are hydrolytically degradable. Three kinds of fiber mats of PGA with different fiber diameters and comparable crystallinities were prepared using an electrospinning method. Our choice of fiber mats was because the ratio of the surface area, where the hydrolytic degradation starts to occur, to the volume was larger than that for the films. Dynamic mechanical analysis (DMA) enabled us to gain direct access to the dynamic glass transition temperature (Tgα) of PGA in the fiber mats both in dry gaseous nitrogen and liquid water. The Tgα value varied not only with the presence of water molecules, but also with the fiber diameter, or the specific surface area. The degradation behavior of PGA fiber mats was examined by immersing the samples in phosphate-buffered saline at various temperatures. When the segmental motion of PGA in the fiber mats was released, the apparent crystallinity of the mats increased, meaning that PGA amorphous chains were cleaved and thus partially eluted into the aqueous phase. It was also shown that partially cleaved chains crystallized.