According to his father Vojo, he came from a Serbian family[1] from Montenegro, which at the end of the 19th century brought to Montenegro the first cinema, the first department store, the first theater, a reading room and a library, a tin orchestra, the first newspapers and magazines.

[2] Šobajić attended primary and secondary school in Belgrade, Istanbul and Nikšić.

He graduated from the Academy of Fine Arts in Belgrade in 1970, and two years later moved to Paris.

Since 2005, he had been teaching at the Luxun Academy of Fine Arts in Shenyang, China, and at the same time founded the Faculty of Art and Design at Megatrend University in Belgrade, where he was dean, full professor and honorary doctor, and in 2012, he became professor emeritus.

Šobajić published his first book, entitled: Paint and be silent, of an autobiographical character, which talks about the influence of globalism on contemporary art, in 2018.