| Season Review | Matches: 1958 – 1959 | 1958-1959 Pictures |
Appearances (Goals in brackets)
* – left Celtic during season 1958/59
† – left Celtic at the end of season 1958/59
| League | League Cup | Scottish Cup | Total | |
| Beattie | 20 | 6 | 0 | 26 |
| Haffey | 14 | 3 | 6 | 23 |
| Kennedy | 1 | 1 | 0 | 2 |
| Donnelly | 4 | 1 | 0 | 5 |
| Mochan | 33 (5) | 8 | 6 | 47 (5) |
| MacKay | 30 | 8 | 6 | 44 |
| Smith | 27 (5) | 3 | 6 | 36 (5) |
| Evans | 19 | 3 | 6 | 28 |
| McNeill | 17 | 6 | 0 | 23 |
| Peacock | 27 (3) | 9 (1) | 6 (1) | 42 (5) |
| Collins * | 2 (1) | 7 (6) | 0 | 9 (7) |
| Higgins † | 10 (3) | 0 | 0 | 10 (3) |
| McVittie | 17 (5) | 0 | 5 (3) | 22 (8) |
| Fernie * | 13 (4) | 9 | 0 | 22 (4) |
| Jackson | 17 (3) | 1 | 4 (1) | 22 (5) |
| Conway | 8 (1) | 7 (4) | 1 | 16 (6) |
| Lochhead | 8 (2) | 0 | 4 (1) | 12 (3) |
| Byrne | 5 (1) | 0 | 0 | 5 (1) |
| Colrain | 25 (14) | 1 (2) | 3 | 29 (19) |
| Divers | 20 (9) | 1 | 4 (2) | 25 (11) |
| Wilson † | 14 (3) | 7 (6) | 5 (5) | 26 (14) |
| Auld | 27 (8) | 9 (6) | 2 | 38 (14) |
| Tully | 5 | 9 (2) | 1 | 15 (2) |
| Slater | 4 (1) | 0 | 0 | 4 (1) |
| Jack † | 1 | 0 | 0 | 1 |
| Kurila | 1 | 0 | 0 | 1 |
| Chalmers | 1 | 0 | 0 | 1 |
| Crerand | 4 | 0 | 0 | 4 |
| Paton | 0 | 0 | 1 | 1 |
| own goals | (2) | (1) | (1) | (4) |