Dinamo is the second Belarusian team, after BATE Borisov, to reach UEFA Europa League group stages (2014–15 and 2015–16).

In the 1984–85 season, Dinamo Minsk reached the quarter-finals of the UEFA Cup after beating HJK Helsinki, Sporting CP and Widzew Łódź, but were eventually stopped by Željezničar Sarajevo.

The 2000s saw Dinamo Minsk failing to secure any league title in the battle against BATE Borisov, thus finishing in lower places.

In 2014, Dinamo Minsk beat MYPA, CFR Cluj and Nacional to be drawn in Group K of UEFA Europa League, along with Italian side Fiorentina, French team Guingamp and Greek side PAOK, becoming the second team, after BATE Borisov, to reach group stages of Europa League.

Dinamo finished at the bottom with four points, after a draw with Guingamp and a historical 2–1 victory over Fiorentina.

The ultras of Dinamo Minsk are famous for their right-wing political orientation and there have been several riots, clashes with the police forces and chants against the Belarusian authoritarian regime, led by long-time President Alexander Lukashenko.

Their political views as well as geographic proximity and contest for dominance of the city make them rivals with neighbours Partizan Minsk, whose fans tend to be strongly left-wing.