Budućnost were the defending champions from the previous season after defeating Lovćen in the final by the score of 4–0.[3]
First round
Draw for the first round was held on 22 August 2019.[4] Ten first round matches were played on 28 August 2019 and one was played on 25 September 2019.[2]
Stadium: Pomoćni teren FK Sutjeska Attendance: 100 Referee: Nikola Vođević
Second round
Draw for the second round was held on 26 September 2019, Jedinstvo received a bye.[5] After the draw, Petnjica withdrew from the competition.[6] Twelve clubs competed in the second round which was played over two legs from 2 to 23 October 2019.[2]
Stadium: Gradski stadion Attendance: 500 Referee: Savo Vujović
Interruption
Montenegrin Cup was interrupted in March 2020, before the semi-finals, due to the coronavirus pandemic. Semifinalists were FK Budućnost, FK Sutjeska, FK Podgorica and OFK Petrovac.
Three months after that, Football Association of Montenegro decided that Montenegrin Cup for the season 2019-20 won't be continued, as all official competitions were suspended.[1]