Referee John Beaton said after the game: "We came out midway through the half to see what it was looking like at pitch level.
"At that point it probably looked ok.
"I spoke to both managers at the start of the second half and obviously came back out with the intention that we would start the game and see how we got on.
"But the Motherwell fans told us that they couldn't see the game, so that was the first sign of a problem.
"Then both the assistant referees told me they couldn't see the opposite side of the field so that obviously then becomes a problem for offside decisions.
"For me at that point it was actually not too bad in the middle of the field.
"But the first time the ball went into the air I couldn't pick it out coming out the sky.
"So I obviously stopped it, probably less than two minutes into the second half, spoke to both managers, decided we would give it 10 minutes to see how it went.
"But it was just getting worse. I think we were prolonging the situation by continuing and giving Kilmarnock the opportunity to activate the abandonment procedure and make sure the stewards were in place to get it done properly.
"And then I told both managers and they seemed happy and content with the decision.
"It was difficult to see. The Motherwell manager was pointing out that it was difficult to see the ball from a distance. And he was right because the first time it went into the air it was quite difficult to pick it coming back down.
"It could have presented itself as a safety issue. We've got a responsibility to the paying fans as well and if they can't see the fans then it just becomes a bit farcical."
During the 46 minutes that were played, Motherwell's Curtis Main produced a thrilling early first half run into the Killie box but his through ball was overhit and ran out for a goal kick.
Killie responded quickly and an Eamonn Brophy surge at the other end preceded him shooting just wide from outside the box.
Motherwell then missed a sitter on 21 minutes when defender Tom Aldred - wearing a Basil Fawlty-esque bandage - somehow headed David Turnbull's free-kick from the right wide from a great central position.
A great run by Gboly Ariyibi was halted by a robust Kirk Broadfoot challenge. A corner was then cleared to Ariyibi whose low drive from 20 yards was saved by keeper Daniel Bachmann.
Liam Grimshaw's 29th minute cross from the right was cleared to Turnbull whose drive was inadvertently blocked by his own player Main.
A close call from the hosts on 41 minutes saw Brophy's powerful long range volley blocked by Gillespie.
But that was it for the action as the fog swirled in incredibly quickly and led to the abandoment.
A decision will be made tomorrow (Thursday) on when to restage the game.
Motherwell: Gillespie, Tait, Aldred, Campbell, Main, Ariyibi, Grimshaw, Dunne, Gorri, Turnbull, Hastie.
Referee: John Beaton