Babunski was born in
Skopje,
SR Macedonia,
Socialist Federal Republic of Yugoslavia. 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. After two solid years in the
Spanish second division with
Lleida he played the same time in Japan, at
Gamba Osaka. On 31 July 1998 Babunski was transferred to the Greek side,
AEK Athens for a fee of 330 million
drachmas. He failed to establish himself in the squad and on 28 July 1999 he was transferred to
Logroñés. Babunski retired professionally in 2001 at the age of 33, after stints with,
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. ==International career==