This study presents the effect of gamma rays of up to 2000 kGy on the chemical structure and the physical properties of a poly(butylene adipate-co-terephthalate) (PBAT) with 48% mol of terephthalic units. PBAT is a polymer with properties similar to polyethylene (PE) but it is biodegradable and not toxic to the environment, and it can be prepared with a renewable content of up to 68.6% weight, with uses in biomedicine and packaging. Previous studies found in the literature have been conducted using low doses and the results were contradictory. The results for gel content and crosslinking efficiency were in agreement with the results found in the literature. Molecular weight decreased and widened with the increase in dose. Proton NMR analysis was used for the first time in PBAT to determine the changes in chemical species, the formation of new chemical species, and the bonds more susceptible to be broken by gamma rays. Both thermal and mechanical properties were explained by the scission of the chains in the amorphous phase and at the boundaries of the crystallites. The thermal parameters most affected by irradiation were the crystallization temperature and temperature of melting after cooling from the melt. Stress and strain at break suffered a continuous decrease with dose until PBAT became fragile at high dose.