However, Wickham scored his first goal of the game just six minutes later to level the scores, curling the ball in from a tight angle.
The on-loan striker put the home side ahead for the first time later in the first half, spotting Kasper Schmeichel off his line as the Foxes tried to clear a corner.
Wickham could have completed his hat-trick before the break, creating another couple of chances before the half-time whistle, while Jamie Vardy came close to finding an equaliser for the visitors.
David Nugent hit two quick-fire efforts at the start of the second half as the visitors looked to get back into the game, but his first was saved before he tapped the rebound wide.
Leicester continued to create the majority of the chances, with Nugent and Ignasi Miquel looking the most likely to provide the equalising goal.
Atdhe Nuhiu set up Wickham for a chance to add his third of the game, but the striker's finish was deflected behind for a corner.
Chris Wood came off the bench and tested Damian Martinez late on as the league leaders continued to search for their second goal of the night, but they could not get back on level terms before full time.
The result leaves the Foxes top of the table, level on points with Queens Park Rangers, while the Owls sit in the relegation zone.