On the club level he started playing with hometown's FK Vardar, then spent two seasons in Bulgaria with CSKA Sofia to become of the first Macedonians to compete in the A Football Group.

Babunski retired professionally in 2001 at the age of 33, after stints with AEK Athens, Logroñés, Sint-Truiden and Chemnitzer FC – he left Germany in December 2000, signing with native FK Rabotnichki – the second and the last teams two also in the respective countries' second level.

Babunski began his coaching career as assistant in the Macedonian national side, under Slobodan Santrač.

When the latter resigned on 23 August 2005 he was appointed interim manager but, on 17 February of the following year, Srečko Katanec took over the job on a permanent basis.

On 23 July 2009, Babunski was signed as head coach of Macedonian First Football League champions Rabotnichki, also from Skopje, winning the domestic cup in his sole season.