Barcelona Born in
Skopje, Babunski joined
FC Barcelona's
La Masia in 2006, aged 12, after starring at
UDA Gramenet. In December 2011, he was elected Macedonian Young Sportsperson of the Year, ahead of
karatekas Aziz Ismail and Berat Jakupi. Babunski was promoted to
the reserves in June 2013, and made his professional debut on 24 August, coming on as a second-half
substitute in a 2–1 home win against
CD Lugo in the
Segunda División championship. He scored his first goal on 31 May 2014, netting a
last-minute winner in a 4–3 home success over
AD Alcorcón. He played 16 games in
2014–15, a campaign which ended with relegation to
Segunda División B. On 28 February 2015, as a half-time substitute for
Juan Cámara, he received a straight red card in a 2–4 loss to
RCD Mallorca at the
Mini Estadi. After a decade in the ranks of Barcelona, Babunski left by mutual consent in January 2016.
Red Star Belgrade Babunski signed a -year deal with
Red Star Belgrade on 28 January 2016. He made his
Serbian SuperLiga debut on 20 February, replacing
Aleksandar Katai for the final 11 minutes of a 2–1 home win over
FK Mladost Lučani, and played five more matches as the team
won their 27th title.
Japan On 30 January 2017, Babunski signed for Japanese club
Yokohama F. Marinos, as their second purchase from Red Star that month after that of
Hugo Vieira. He made his debut in the
J1 League on 25 February, scoring the first goal of a 3–2 home win over
Urawa Red Diamonds in the
season opener. In August 2018, Babunski signed for
Omiya Ardija, in the same league.
Romania On 2 March 2020, Babunski signed a one-and-a-half-year contract with Romanian club
FC Botoșani. On 29 December, he was released from the club by mutual consent. On 11 January 2021, Babunski joined
FC Viitorul Constanța also of
Liga I on a two-and-a-half-year contract.
Hungary On 8 July 2021, Babunski signed a two-year deal with Hungarian club
Debreceni VSC. In the summer of 2022, Debreceni VSC terminated his contract by mutual consent. On 20 September 2022, Babunski signed with
Mezőkövesd, and in January 2023 signed a new two-and-a-half-year contract with the club.
Dundee United On 16 July 2024, Babunski signed for
Scottish Premiership side
Dundee United on a one-year deal with the option for a further season. ==International career==