Darko Plećaš enrolled in the School of Medicine at Belgrade University in 1971, from which he graduated on April 29, 1977 with the average grade 9.53/10. He joined the Clinic for Gynecology and Obstetrics, Clinical Centre of Serbia in 1979. He passed his certifying exam in gynecology and obstetrics in 1984 and he completed his sub-specialization in perinatal medicine in 2002. Darko Plećaš defended his master thesis on „The frequency of Rh- Isoimmunization following artificial pregnancy termination“ in 1981, and his doctoral thesis on „The diagnostic procedures in pregnancy and child birth and pregnancy outcomes in Rh-isoimmunized patients“ in 1983, both at the School of Medicine, University of Belgrade.
Darko Plećaš was the Head of Fertility Control Department at the Clinic from 1997-2018, Deputy Director of the Clinic from 2001-2018 and Assistant Director in 2018.
He became a junior teaching assistant at the Department of Gynecology and Obstetrics in 1985 and teaching assistant in 1989; in 1993 he was promoted to the rank of docent, then became associate professor in 1998 and got his full professorship in 2004. From 2003 – 2012, Darko Plećaš was the Head of the Department of Gynecology and Obstetrics (undergraduate studies) and from 2012-2018, he headed the Department of Human Reproduction (graduate studies) at the School of Medicine, Belgrade University.
Darko Plećaš spent the academic year 1988/89 as a Fulbright scholar, when he did his post-doctoral research at the Department of Obstetrics, Gynecology and Reproductive Science, The Mount Sinai School of Medicine, New York.
From 2015-2018, he was a member of the National Council for High Education of Serbia.