The first commercial production of MSA, developed in the 1940s by Standard Oil of Indiana, was based on oxidation of dimethylsulfide by  from air. Although inexpensive, this process suffered from a poor product quality and explosion hazards. 
In 1967, the Pennwalt Corporation (USA) developed a different process for dimethylsulfide (as a water-based emulsion) oxidation using chlorine, followed by extraction-purification. In 2022 this chlorine-oxidation process was used only by Arkema (France) for making high-purity MSA. This process is not popular on a large scale, because it co-produces large quantities of hydrochloric acid. 
Between years 1970 and 2000 MSA was used only on a relatively small-scale in niche markets (for example, in the microelectronic and electroplating industries since the 1980s), which  was mainly due to its rather high price and limited availability. However, this situation changed around 2003, when BASF launched commercial production of MSA in Ludwigshafen based on a modified version of the aforementioned air oxidation process, oxidising dimethyldisulfide with nitric acid which is then restored using atmospheric oxygen. The former is produced in one step from methanol from syngas, hydrogen and sulfur.
An even better (lower-cost and environmentally friendlier) process of making methanesulfonic acid was developed in 2016 by Grillo-Werke AG (Germany). It is based on a direct reaction between methane and oleum at around  50 °C and  100 bar in the presence of a potassium persulfate initiator.  This technology was acquired and commercialized  by BASF in 2019.