| Club: | Celtic |
| Season: | 1944–45 |
| Manager: | Jimmy McStay |
| Stadium: | Celtic Park |
| League: | Southern League |
| League Result: | 2nd |
| Cup1: | Summer Cup |
| Cup1 Result: | Semi-final |
| Cup2: | Southern League Cup |
| Cup2 Result: | Group stage |
| Prevseason: | 1943–44 |
| Nextseason: | 1945–46 |
During the 1944–45 Scottish football season, Celtic competed in the Southern Football League.
See main article: 1944–45 Southern Football League (Scotland).
See main article: 1944–45 Southern League Cup (Scotland).