It was a hard-fought point for Charlton, who confirmed prior to the game they are in takeover talks with Roaland Duchatelet, a Belgian businessman.
The Addicks went ahead three minutes after the break through Dale Stephens - but were pegged back on 59 minutes by Connor Wickham.
For a side which had only won away once all season, Wednesday showed attacking intent with Wickham up front with Chris Maguire.
Wickham, on loan from Sunderland and back in the side after injury, had the first effort on target for Wednesday but the angle was tight and Ben Alnwick took it with ease.
Alnwick took two attempts to gather another effort from Wickham, who escaped the attentions of Cedric Evina.
It was almost third time lucky for Wickham, whose curling free-kick evaded the wall but was kept out by Ben Alnwick.
Play was delayed for a few moments after Stephen McPhail and Yann Kermorgant clashed heads, with the Wednesday defender picking up a booking for the challenge.
Wednesday came close to an opening on the half hour when Roger Johnson hit a looping volley onto the crossbar.
The Addicks had to make do without full-back Rhoys Wiggins, who had missed the match in order to be with his partner, who was giving birth.
Charlton had skipper Johnny Jackson back after injury for the first time in four games and he added steel to the Addicks' midfield.
Kermorgant could have done better with an early second half effort which he hit wide - but the space he was allowed should have alerted Wednesday.
Instead it was exploited moments later as Stephens pounced on a through-ball from Lawrie Wilson. The midfielder steadied himself before planting the ball unchallenged past Chris Kirkland for his third league goal of the campaign.
Wednesday's caretaker manager looked to liven things up with a double substitution, bringing on Jacques Maghoma and Atdhe Nuhiu in the 55th minute.
It worked as Wednesday controversially levelled four minutes later, almost inevitably through Wickham - although there were claims for offside as the striker tapped in from inches out after direct work from Maguire and Kieran Lee.
Wickham also headed powerfully over the bar from a corner and hit another effort wide after being teed up by Lee.
Charlton were left aggrieved when a Cameron Stewart shot was blocked by Kirkland and went behind - but they were denied a corner.
The Owls claimed a penalty when Nuhiu took a tumble in the box but referee Fred Graham was not impressed.
Simon Church had a good opportunity to win the contest for Charlton in time added on - but he fired over the bar unchallenged from 18 yards.