| Club: | Heart of Midlothian |
| Season: | 1884–85 |
| Cup1 Result: | Disqualified |
| Prevseason: | 1883–84 |
| Nextseason: | 1885–86 |
Season 1884–85 was the tenth season in which Heart of Midlothian competed at a Scottish national level, entering the Scottish Cup for the tenth time.
Hearts entered the Scottish Cup at the second round winning their match against Dunfermline. Hearts should have proceeded to the third round but were disqualified for professionalism.[1]
Later that season Hearts reached the fourth round of the Edinburgh Shield losing to Rival Hibernian.[2]
See main article: 1883–84 Scottish Cup.
See main article: East of Scotland Shield.
See main article: Rosebery Charity Cup.