Graham Hill won the Monaco Grand Prix 1963 at Circuit de Monaco on 26 May 1963, starting from P2 on the grid. Richie Ginther finished second for BRM, with Bruce McLaren completing the podium for Cooper-Climax.
| Pos | Grid | Driver | Team | Laps | Time / Status | Pts | FL |
|---|---|---|---|---|---|---|---|
| 1 | 2 | Graham HillHIL | BRM | 100 | 2:41:49.7 | 9 | |
| 2 | 4 | Richie GintherGIN | BRM | 100 | +4.6 | 6 | |
| 3 | 8 | Bruce McLarenMCL | Cooper-Climax | 100 | +12.8 | 4 | |
| 4 | 3 | John SurteesSUR | Ferrari | 100 | +14.1 | 3 | |
| 5 | 10 | Tony MaggsMAG | Cooper-Climax | 98 | +2 Laps | 2 | |
| 6 | 9 | Trevor TaylorTAY | Lotus-Climax | 98 | +2 Laps | 1 | |
| 7 | 11 | Jo BonnierBON | Cooper-Climax | 94 | +6 Laps | 0 | |
| 8 | 1 | Jim ClarkCLA | Lotus-Climax | 78 | Gearbox | 0 | |
| 9 | 16 | Jack BrabhamBRA | Lotus-Climax | 77 | Gearbox | 0 | |
| R | 5 | Innes IrelandIRE | Lotus-BRM | 40 | Accident | 0 | |
| R | 7 | Willy MairesseMAI | Ferrari | 37 | Gearbox | 0 | |
| R | 14 | Maurice TrintignantTRI | Lola | 34 | Clutch | 0 | |
| R | 6 | Dan GurneyGUR | Brabham | 25 | Differential | 0 | |
| R | 13 | Jim HallHAL | Lotus-BRM | 20 | Gearbox | 0 | |
| R | 12 | Jo SiffertSIF | Lotus-BRM | 3 | Engine | 0 | |
| W | 0 | Chris AmonAMO | Lola | 0 | Withdrew | 0 | |
| F | 0 | Bernard CollombCOL | Lotus-Climax | 0 | Did not qualify | 0 | |
| W | 0 | Phil HillHIL | ATS | 0 | Withdrew | 0 | |
| W | 0 | Giancarlo BaghettiBAG | ATS | 0 | Withdrew | 0 | |
| W | 0 | John Campbell-JonesCAM | Lotus-BRM | 0 | Withdrew | 0 | |
| W | 0 | Ian BurgessBUR | Scirocco | 0 | Withdrew | 0 | |
| W | 0 | Tony SettemberSET | Scirocco | 0 | Withdrew | 0 | |
| W | 0 | Nasif EstéfanoEST | De Tomaso | 0 | Withdrew | 0 | |
| W | 0 | Lorenzo BandiniBAN | BRM | 0 | Withdrew | 0 | |
| W | 0 | Carel Godin de BeaufortDEB | Porsche | 0 | Withdrew | 0 |