Noise pollution is one of the harmful physical sources in the textile industry, which is among those industries that are faced with noise exposure problems. The results of environmental sound measurements at modern textile mills have shown that the sound pressure level varied from 95 to 130 dB, where the highest sound pressure level was at weaving machines. Textile insulation materials can be fitted in order to decrease sound pollution at a low cost. The objective of this work is to design a sound absorber that can be fixed to the body of the machines, at the point of the noise generation, to reduce noise pollution. Poly(lactic acid) (PLA), which is an environmentally friendly material, was used to produce different samples of meltblown nonwoven absorbers to be used for damping the noise of textile machinery. PLA meltblown nonwoven fabric with the areal density of 16.7 g/m2, average fiber diameter of 1.1 µm, mean pore diameter of 9.8 µm and thickness of 0.27 mm exhibited significant sound absorption. The sample with the smallest average fiber diameter among those investigated had the highest damping effect: 23.95, 41.29 and 29.32 dBA at frequencies of 400, 1000 and 1500 Hz, respectively. Our goal is to have a practical tool that accurately evaluates the absorber sound damping under the actual running conditions of the textile machinery. The design of the absorber from one layer of the PLA meltblown nonwoven over a rigid polyurethane foam sheet had an excellent sound absorption property.