The defending World Champion clocked 1:11.767 to take his 87th pole, ahead of Red Bull's Max Verstappen (1:12.113) and Mercedes teammate Valtteri Bottas (1:12.129) on Saturday.
"I do not know really how we did it today," the 34-year-old Briton said on the F1 Twitter account.
"I am not quite sure what happened to the Ferraris. It is so important to us, at our second home Grand Prix," he added
Vettel of Germany failed to set a time in Q1 of the qualifying and will start his home race from the back of the grid.
"I do not know what happened. Something was broken with the turbo. It is bitter for us. The car feels great and we have missed a big opportunity here," he said.
Leclerc of Monaco gave a good performance in Q1 and Q2, but could not leave the garage in Q3 and is set to start in the tenth position, reported Efe news.
"I have no idea if it was the same issue as Sebastian, on my side it was a fuel system problem," he said.
Finland's Kimi Raikkonen placed his Alfa Romeo in the fifth position, with Haas driver Romain Grosjean in the sixth.
Spain's McLaren driver Carlos Sainz will take off from the seventh, while Racing Point's Sergio Perez of Mexico is to start in eighth and Renault's Nico Hulkenberg in ninth.
The top-10 drivers in the timesheet are as follows:
1. Lewis Hamilton (Britain / Mercedes) 1: 11.767
2. Max Verstappen (Holland / Red Bull) +0.346
3. Valtteri Bottas (Finland / Mercedes) +0.362
4. Pierre Gasly (France / Red Bull) +0.755
5. Kimi Raikkonen (Dinland / Alfa Romeo) +0.771
6. Romain Grosjean (France / Haas) +1.084
7. Carlos Sainz (Spain / McLaren) +1.130
8. Sergio Pérez (Mexico / Racing Point) +1.298
9. Nico Hulkenberg (Germany / Renault) +1.359
10. Charles Leclerc (Monaco / Ferrari) No time.
( With inputs from IANS )