| Club: | Hibernian |
| Season: | 1884–85 |
| Cup1: | Scottish Cup |
| Cup1 Result: | Semi-finalists |
| Prevseason: | 1883–84 |
| Nextseason: | 1885–86 |
Season 1884–85 was the 9th season in which Hibernian competed at a Scottish national level, entering the Scottish Cup for the 8th time.
Hibs reached the semi-final of the Scottish Cup, losing 2–1 to the Renton.
All results are written with Hibs' score first.
| Date | Round | Opponent | Venue | Result | Attendance | Scorers | |
|---|---|---|---|---|---|---|---|
| 13 September 1884 | R1 | Bo'ness | A | 2–0 | |||
| 4 October 1884 | R2 | Vale of Teith | H | 5–1 | |||
| 25 October 1884 | R3 | Glengowan | H | 5–1 | |||
| 15 November 1884 | R4 | Ayr | H | 5–1 | |||
| 6 December 1884 | R5 | Morton | H | 4–0 | |||
| 27 December 1884 | R6 | Annbank | H | 5–0 | |||
| 24 January 1885 | SF | Renton | H | 2–3 | 7,000 |