Lafferty has received a club fine after a video, which appeared on social media, showed the former Rangers and Hearts striker reacting when a man posing for a photo with him says “Up the Celts”.
The 35-year-old faces an SFA tribunal on October 20 accused of not acting in the best interests of football and breaching a rule which forbids the use of insulting language which includes reference to the likes of ethnic origin, race, nationality, religion or belief.
SFA rules state that the punishment for the latter is a mandatory minimum 10-match ban which can only be reduced “where exceptional circumstances are established”.
Killie announced their internal investigation into the incident had been concluded shortly after the SFA charges were announced.
A statement added: “The club can confirm that Kyle regrets his actions and acknowledges that he has let down himself, his family, the club and the supporters.
“Kilmarnock Football Club has subsequently taken internal action, including the serving of a substantial fine.
“The club has also engaged Scotland’s leading anti-sectarian charity, Nil By Mouth, which will work closely with Kyle on a one-to-one basis, in addition to delivering training to our first team squad and academy squad members, to provide education which the charity believes is key to tackling sectarianism in society.
“Kyle has also committed to supporting the club’s community projects which will see him participating in Nil by Mouth’s educational initiatives, in addition to serving Kilmarnock’s ‘Football for All’ programmes on a weekly basis for the foreseeable future.”
The club added they would co-operate fully with the SFA’s investigation.
Lafferty was axed from the Northern Ireland squad for their recent Nations League fixtures against Kosovo and Greece, with manager Ian Baraclough stating that a back injury had also been considered when the decision was made.
The former Motherwell manager claimed the incident was not necessarily the end of Lafferty’s international career.
It is unclear whether Lafferty will be in the squad for Kilmarnock’s cinch Premiership match at Aberdeen on Saturday.
Killie manager Derek McInnes earlier stated the club would be guided by the SFA’s input but Lafferty could feature if fit considering he is likely to face some form of suspension following his Hampden hearing.
McInnes is looking forward to returning to Pittodrie for the first time since leaving in 2021 after eight years in charge.
He said: “I didn’t get the chances to say goodbye to everybody, but I appreciate the time I was there. Eight years, almost 400 games. It was a big part of my life. I worked with a lot of very good players.
“We had four second-placed finishes and it should have been five if the referee does his job right in the last game of the season (2014). So there is a lot goes into that.
“We didn’t do that by spending money, we didn’t do it by throwing big wages away. We did it by sheer hard work, a real togetherness, really good recruitment and hungry players. We had a brilliant spirit and we reinvented the squad time and time again to meet the demands. It was a collective effort.
“I had a brilliant time there, but I am going there as Kilmarnock manager and it’s business. I am going to try to get a result. I am looking forward to it.”