No.
Per Wikipedia MSG is produced today by bacterial fermentation. At one point it was made synthetically from acrylonitrile, which itself is produced from propylene, which in turn is generated through natural fermentation.
I did find this paper which referenced a couple of Japanese books from the 1970s where the MSG from petroleum claim was made. It appears to me that these books were more of a reactionary diatribe against the packaged foods industry in general, which undermines the credibility of the author and his claims.
In two books, Diagnosing Ajinomoto (Ajinomoto o
shindan suru) and The Japanese and Ajinomoto (Nihonjin
to Ajinomoto), he [Gunji Atsutaka] recounted the most alarming portions of
American medical reports, accused the company of concealing
toxic impurities, and claimed msg was being made
from petroleum. These accusations, however, were merely
the preamble to a larger polemic against mass-produced
convenience foods in general, which Gunji deplored precisely
for their convenience. As he put it in the preface to his
second book: “The frightening thing about processed foods
made by large corporations, in addition to the toxicity of
the large quantities of food additives used, is that they cause
the spiritual ruin of Japanese women.” Unlike the rest of
humanity and unlike other animals, Gunji asserted, Japanese
and Americans happily ate food prepared by others, “as
if they were prisoners.” Japanese women had an obligation
to master the food resources of nature and to cultivate
the skills to make food delicious without the assistance of
ready-made ingredients. “[As long as] housewives continue
to make meals every day,” he wrote, “praying in their hearts
that their families will always be healthy, therein lies spiritual
progress, ensuring a bright and peaceful life.” This,
he explained, was why he had written books urging readers
not to eat Ajinomoto products.41 In effect, Gunji’s critique
took the very promise of rationality and convenience that
Ajinomoto had been making to Japanese housewives since
1909 and turned it against both the company and the housewives
themselves.