Silver nanoparticles (AgNPs) are of great interest due to their antimicrobial, optical and catalytical properties. Green synthesis of AgNPs is fundamental for some applications such as biomedicine and catalysis. Natural polymers, such as chitosan, have been proposed as reducing and stabilizing agents in the green synthesis of AgNPs. Physico-chemical properties of chitosan have a great impact on its technological and biological properties. In this paper, we explore the effect of chitosan molecular weight (Mw) on the thermal AgNPs production using two sample sets of low Mw chitosans (F1 > 30 kDa, F2: 30⁻10 kDa and F3: 10⁻5 kDa) produced by enzymatic depolymerization of a parent chitosan with chitosanase and lysozyme. Both polymer sets were able to effectively reduce Ag to Ag as the presence of the silver surface plasmon resonance (SRP) demonstrated. However, the ability to stabilize the nanoparticles depended not only on the Mw of the polymer but particularly on the polymer pattern which was determined by the enzyme used to depolymerize the parent chitosan. Low Mw chitosan samples produced by lysozyme were more effective than those produced by chitosanase to stabilize the AgNPs and smaller and less polydisperse nanoparticles were visualized by transmission electron microscopy (TEM). With some polymer sets, more than 80% of the AgNPs produced were lower than 10 nm which correspond to quantum dots. The preparation method described in this paper is general and therefore, it may be extended to other noble metals, such as palladium, gold or platinum.