The supporter ran onto the pitch from the away end before striking the former Liverpool goalkeeper on his blind-side, leaving him on the floor and needing treatment.
The first Yorkshire derby between the two sides in five years was marred by the assault, which came just after Leeds had equalised through a Michael Tonge strike on 80 minutes.
The fan escaped back into the mass of Leeds support before stewards or police could detain him, though pictures of his face have already been posted on social networking website Twitter.
"I'm embarrassed to be the Leeds manager tonight," Leeds boss Neil Warnock said after the game.
"He's a moron, an idiot. I don't mind rivalry but this guy should be made an example of, prosecuted and be put in prison.
"The guy who done this has the mentality of a five year-old. He's spoilt the night for everybody, as it was a good atmosphere here up to that point."
Wednesday manager Dave Jones was quick to condemn the Leeds support after also taking issue with some of the chants from the away end.
"Vile animals they are [the Leeds fans]," Jones said. "The authorities have to do something, or these people will keep doing this. They were all chanting, so they shouldn't have been applauded afterwards.
"They want to come onto the pitch and punch my goalkeeper? They should be banned from every ground in the league."
Leeds were quick to issue the following statement after the game, condemning the actions of the supporter and promising to take action against him.
"Leeds United Football Club would like to publicly apologise and condemn the action of the fan who came on the pitch and attacked Sheffield Wednesday goalkeeper Chris Kirkland. The club will fully co-operate with the police and the football authorities in identifying the individual concerned.
"After the week football has endured there is no place for this type of behaviour and the majority of Leeds supporters will be ashamed of his actions."