Sajnovics was born in Tordas. He was a pupil of the astronomer and mathematician Maximilian Hell. When Hell planned an expedition to observe the transit of Venus in Vardø, northern Norway in June, 1769, he took Sajnovics with him. Hell had heard that the Hungarian and Lapp (Sami) languages were related and thought that Sajnovics, as a native Hungarian speaker, would be able to investigate the connection. He died, aged 51, in Pest.
Sajnovics published the results of his research in his Demonstratio idioma Hungarorum et Lapporum idem esse (1770), which was a breakthrough in the study of Uralic languages. Sajnovics's ideas were further developed by Samuel Gyarmathi.