| Club: | Hibernian |
| Season: | 1887–88 |
| Cup1: | Scottish Cup |
| Cup1 Result: | R3 |
| Prevseason: | 1886–87 |
| Nextseason: | 1889–90 |
Season 1887–88 was the 12th season in which Hibernian competed at a Scottish national level, entering the Scottish Cup for the 11th time.
Hibs reached the third round of the Scottish Cup, losing 6–2 to the Heart of Midlothian.
All results are written with Hibs' score first.
| Date | Round | Opponent | Venue | Result | Attendance | Scorers | |
|---|---|---|---|---|---|---|---|
| 3 September 1887 | R1 | Broxburn Thistle | H | 5–0 | |||
| 24 September 1887 | R2 | Erin Rovers | A | 6–0 | 1,000 | ||
| 15 October 1887 | R3 | Heart of Midlothian | A | 1–1 | 6,000 | ||
| 22 October 1887 | R3 R | Heart of Midlothian | H | 1–3 | 8,500 |