Kilmarnock Football Club Supporters Association agreed to the businessman's request to attend - as other directors have done so in the past.
It invited, "in the interests of fairness", a group of shareholders who want Johnston to resign.
But the group rejected the offer to attend Saturday's meeting at the club.
At a hostile annual meeting of the Scottish Premiership club in April, there were calls for Johnston, the former club chairman, to resign.
And disgruntled shareholders are in the process of calling an extraordinary meeting to vote on Johnston's position as company secretary.
"That group indicated that they felt that the appropriate forum for any discussion and debate would be the anticipated EGM and would not be sending any representative on Saturday," said a KFSA statement.
"However, they specifically stated that they would have no objection to Michael Johnston attending on Saturday and taking part in a question and answer session which was being considered by the committee.
"The committee appreciated that there would be criticism however this sensitive matter was dealt with.
"On balance, it was felt that fans, who may not be shareholders, will now have the opportunity of asking their own questions of Mr Johnston.
"It is hoped, and expected, that the question and answer session can be conducted in a civil and courteous manner regardless of differing views and opinions."
Under fire Kilmarnock director Michael Johnston will face fans' questions at this weekend's annual meeting of the club's supporters association.