The Northern Irishman landed himself in trouble after describing Celtic as "the monster of Scottish football" following a row with Hoops boss Neil Lennon, but Killie chairman Johnston says the failure of Shiels' team to reach performance targets means his role as manager will now be re-examined.
Kilmarnock finished ninth in the Clydesdale Bank Premier League despite needing just one win from their final two games before the split to clinch a top-six slot.
Johnston told the BBC: "Kenny's position is under review at present. This is due to his failure to meet a contractual performance-related target and potential breaches of contract relating to media comments and observance of Scottish FA articles and rules and SPL articles and rules."
Shiels became involved in a public row with Lennon over the PFA Scotland player of the year shortlist, with the Parkhead manager complaining that none of his players had been nominated for the main award.
The Ayrshire outfit's manager then gave an interview with BBC Radio Scotland at the end of April in which he said: "They have got a massive influence in the judicial panel and things like that, decisions that's made. Celtic are the monster of Scottish football.''
The Killie manager was accused of both bringing the game into disrepute and not acting in the best interests of football by making comments that "call into question the impartiality of the Judicial Panel and the integrity of another member club of the Scottish FA".
He was found guilty of the charge and handed a four-match ban, with two of those suspended until the end of next season.
His club were also found guilty of failing to ensure that Shiels complies with Scottish Football Association protocol.
Kilmarnock were in the driving seat for a top-six finish but could only manage one point from two home matches against St Mirren and Dundee in the final pre-split fixtures. And they slumped to four defeats in the five post-split games.