He studied Czech, Russian, Serbo-Croatian, and advanced Indo-European studies at the Faculty of Arts in Brno. He worked at the Brno branch of the academic Institute of the Czech Language (ÚJČ), and in 1958, he moved to the Faculty of Arts in Brno, where he served as dean (1960–1962). In 1971, for political reasons, he was transferred back to the academic ÚJČ in Brno with a publication ban. He published his scholarly works in the internal prints of institutes and (illegally) under the names of his colleagues and pseudonyms. At the end of 1989, he was rehabilitated and reinstated as a professor at the Faculty of Arts in Brno and became the rector of Masaryk University (1990–1992). Jelínek's research efforts were predominantly focused on modern Czech language from the National Revival to the present. His research concentrated mainly on the areas of stylistics, word formation, and syntax. He contributed to extensive works of Czech (and Slovak) lexicography (such as the Slovník spisovného jazyka českého and the Slovník slovenského jazyka). He developed his own concept of stylistics in the chapter Stylistika in the collective work Příruční mluvnice češtiny (1995). Methodologically, he drew from the functional conception of language in the spirit of the Prague School and further developed it independently, informed by the theoretical results of Russian and French stylistic schools. He also paid systematic attention to purism (on which he wrote a synthetic study in Kapitoly z dějin současné jazykovědné bohemistiky, 2007) and to issues of linguistic correctness and culture.

L.: D. Šlosar, ČJL 43, 1992–93, 141–142; (bibliography), SPFFBU A 41, 1993, 141–147; J. Kraus, NŘ 76, 1993, 221–222; Karlík, P. – Krčmová, M. (eds.): Jazyk a kultura vyjadřování. Milanu Jelínkovi k pětasedmdesátinám, B. 1998 (biographical medallion by M. Krčmová and the jubilee’s bibliography); P. Karlík, NŘ 81, 1998, 157–159; J. Zeman, Češtinář 13/5, 2002–2003, 129–130; M. Krčmová, ČJL 53, 2002–2003, 241–243; Prof. Milanu Jelínkovi k 80. narozeninám (= Sborník prací Filozoficko-přírodovědecké fakulty Slezské univerzity v Opavě, ř. jazykovědná D 3), Op. 2003; M. Křístek, SPFFBU A 51, 2003, 249–252 (and bibliography on pp. 252–255); H. Šindlerová, NŘ 86, 2003, 157–160 (with supplements to the bibliography); A. Zura, Bohemistyka 3, 2003, 281ff.; E. Minářová, Bohemistyka 3, 2003, 356ff.