The former England international was struck in the face by a spectator who entered the pitch from the Leeds United section of supporters during Friday's Championship match
Aaron Cawley, from Cheltenham in Gloucestershire, was also found guilty of entering the field of play from the Leeds United section of supporters at Hillsborough during a Championship match on Friday evening.
The game was televised live on Sky Sports, who caught the incident on camera immediately after Leeds had scored an equalising goal in the second half.
Kirkland was standing in his penalty area when he was struck in the face by a man who then ran back into the crowd.
The 31-year-old fell to the ground and needed treatment from the club physio but was able to continue and complete the final 14 minutes of the 1-1 draw.
"I was sore and, as I say, really shocked at what had happened and it was a strange feeling because of all the adrenalin you feel in such a big match anyway," Kirkland told Sheffield Wednesday's official website after the incident.
"The rest of the game flew by and then the final whistle came, the adrenalin goes and you reflect on something like that and it was scary.
"I thought of my family watching something like that and it was not a nice feeling to think my daughter saw me assaulted like that.
"So I'm not seeking publicity on the back of this because I am not that kind of person. I just want the authorities to look at what happened and take the appropriate action because sooner or later, we could be talking about something even more serious."
Leeds United condemned the fan, stating that he will be banned for life from Elland Road, and that they felt his jail sentence should have been longer.
A club spokesman said: "We are pleased to see the matter dealt with by the courts so quickly. We note that he has been given a 16-week jail sentence and a five-year banning order.
"The club will also ban the individual for life from Elland Road when this banning order expires.
"While we are pleased to see justice brought so quickly, our one disappointment is that we feel the sentence could, and should, have been considerably longer."