The draw was made by Estonian Football Association on 18 May 2013, before the 2012–13 final of the same competition. League level of the club in the brackets. Rahvaliiga is a league organized by Estonian Football Association, but not part of the main league system. !colspan="3" align="center"|28 May !colspan="3" align="center"|3 June !colspan="3" align="center"|4 June !colspan="3" align="center"|5 June !colspan="3" align="center"|6 June !colspan="3" align="center"|8 June !colspan="3" align="center"|9 June !colspan="3" align="center"|11 June !colspan="3" align="center"|12 June !colspan="3" align="center"|13 June !colspan="3" align="center"|16 June !colspan="3" align="center"|18 June !colspan="3" align="center"|19 June !colspan="3" align="center"|20 June !colspan="3" align="center"|26 June !colspan="3" align="center"|2 July
Byes
These teams were not drawn and secured a place in the second round without playing:
The draw for the second round was made on 14 June. !colspan="3" align="center"|1 July !colspan="3" align="center"|2 July !colspan="3" align="center"|3 July !colspan="3" align="center"|4 July !colspan="3" align="center"|5 July !colspan="3" align="center"|9 July !colspan="3" align="center"|10 July !colspan="3" align="center"|15 July !colspan="3" align="center"|16 July !colspan="3" align="center"|17 July !colspan="3" align="center"|18 July !colspan="3" align="center"|20 July !colspan="3" align="center"|22 July !colspan="3" align="center"|23 July !colspan="3" align="center"|24 July !colspan="3" align="center"|30 July !colspan="3" align="center"|6 August !colspan="3" align="center"|13 August
Third round
The draw for the third round was made on 18 July. !colspan="3" align="center"|6 August !colspan="3" align="center"|7 August !colspan="3" align="center"|8 August !colspan="3" align="center"|13 August !colspan="3" align="center"|15 August !colspan="3" align="center"|20 August !colspan="3" align="center"|28 August !colspan="3" align="center"|4 September !colspan="3" align="center"|11 September !colspan="3" align="center"|22 October
Fourth round
The draw for the fourth round was made on 15 August. !colspan="3" align="center"|4 September !colspan="3" align="center"|11 September !colspan="3" align="center"|25 September !colspan="3" align="center"|5 October !colspan="3" align="center"|16 October !colspan="3" align="center"|12 November
Quarter-finals
The draw was made on 28 February 2014. Levadia got bye to the semi-finals as the eighth quarter-finalist, Tammeka II, was disbanded after the 2013 league season.
