In May 2013 Baboglo played for the
Ukraine U17 team in a UEFA Development Tournament which took place in Minsk. He won the
Valeriy Lobanovskyi Memorial Tournament in 2019 with the
Ukraine U21 team and played in
2021 UEFA European Under-21 Championship qualification, scoring a goal against
Northern Ireland. In March 2023 Baboglo was called up to
Moldova national football team, but he wasn't able to leave Ukraine. He made his debut for Moldova on 17 June 2023 in a 2–0 loss to
Albania in
UEFA Euro 2024 qualifying. Three days later he scored the winning goal in a 3–2 win over
Poland.{{cite web|publisher=BBC Sport|first=Emlyn|last=Begley|url=https://www.bbc.com/sport/football/65907771|title=Moldova 3-2 Poland: World's 171st-best team fight back for shock win ==International goals==