Wednesday forward Jon Shaw hit the post two minutes later, while City's closest effort was a Jamie Forrester shot that scraped the top of the bar in the second half, but Kevin Pressman was never tested.
Andy Dawson played 45 minutes in his comeback from injury before being rested for the second half with Alistair Benson coming on.
Wednesday's neighbours Sheffield United are next up for City, visiting Boothferry Park on Wednesday.
City line-up: Kuipers; Wiseman, Burton, Holt, Dawson (Benson 45); O'Neil, Russell, Melton, Peat; Webb (Cattermole 71), Forrester.
Un-used subs: Harvey, Cooper, Byron.