| Club: | Celtic |
| Season: | 1963–64 |
| Manager: | Jimmy McGrory |
| Stadium: | Celtic Park |
| League: | Scottish Division One |
| League Result: | 3rd |
| Cup1: | Scottish Cup |
| Cup1 Result: | Fourth round |
| Cup2: | Scottish League Cup |
| Cup2 Result: | Group stage |
| Cup3: | European Cup Winners' Cup |
| Cup3 Result: | Semi-finalists |
| Prevseason: | 1962–63 |
| Nextseason: | 1964–65 |
During the 1963–64 Scottish football season, Celtic competed in Scottish Division One.
See main article: 1963–64 Scottish Division One.
See main article: 1963–64 Scottish Cup.
See main article: 1963–64 Scottish League Cup.
See main article: 1963–64 European Cup Winners' Cup.