Both teams showed plenty of endeavour at the King Power Stadium, but a lack of composure in the final third meant neither could break the deadlock.
The stalemate will cause further concern for Leicester manager Nigel Pearson, who spoke in the build-up of the need to "reignite the confidence" at the club.
The second half proved a more lively affair, and Leicester's Matty James should perhaps have done better when one-on-one with Costel Pantilimon, while Fletcher was once again denied by Schmeichel.
In a bid to end Leicester's barren run in front of goal, Pearson named an attack-minded XI, with Riyad Mahrez and Paul Konchesky coming in after the 2-0 loss at Southampton before the international break.
Mahrez was the focal point in the hosts' lively start and he orchestrated the first meaningful opening in the 13th minute with an intricate throughball that picked out Jeffrey Schlupp, whose shot from a tight angle hit the side-netting.
Sunderland were initially guilty of sloppy errors but they soon grew into the game and Fletcher - passed fit after missing Scotland's friendly defeat to England on Tuesday with a knock - was denied by a smart stop from Schmeichel when clean through against the Leicester goalkeeper.
Schmeichel was called into action again just before the half-hour mark when he got down well to keep out Johnson's low and dipping strike from 30 yards that would have found the bottom corner but for the shot-stopper's intervention.
The away side's pressure continued after the break and Fletcher could have scored when he fired over the crossbar from just inside the area from Sebastian Larsson's clever low corner in the 48th minute.
Gus Poyet's men also had chances, Schmeichel once again foiling Fletcher with a save at his near post after the striker broke down the left in the 70th minute.
David Nugent and Cambiasso were guilty of getting in each other's way in a promising position for Leicester late on, but there was no way through.
