A method for forming biodegradable fibers is provided. The method includes blending polylactic acid with a polyepoxide modifier to form a thermoplastic composition, extruding the thermoplastic composition through a die, and thereafter passing the extruded composition through a die to form a fiber. Without intending to be limited by theory, it is believed that the polyepoxide modifier reacts with the polylactic acid and results in branching of its polymer backbone, thereby improving its melt strength and stability during fiber spinning without significantly reducing glass transition temperature. The reaction-induced branching can also increase molecular weight, which may lead to improved fiber ductility and the ability to better dissipate energy when subjected to an elongation force. To minimize premature reaction, the polylactic acid and polyepoxide modifier are first blended together at a relatively low temperature(s). Nevertheless, a relatively high shear rate may be employed during blending to induce chain scission of the polylactic acid backbone, thereby making more hydroxyl and/or carboxyl groups available for subsequent reaction with the polyepoxide modifier. Once blended, the temperature(s) employed during extrusion of the blended composition can be selected to both melt the composition and initiate a reaction of the polyepoxide modifier with hydroxyl and/or carboxyl groups of the polylactic acid. Through selective control over this method, the present inventors have discovered that the resulting fibers may exhibit good mechanical properties, both during and after melt spinning.