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."