Kiradech returned to the Kuala Lumpur Golf and Country Club to card a four-under-par 68 in the second round after storms had brought play to an early close on Thursday and Friday.
But the leaders managed just two holes of their third round before play was suspended for the third day in succession prompting organisers to cancel the fourth round.
Aphibarnrat has a one shot lead over playing partner Charl Schwartzel and the third and final round will resume on Sunday morning at 9:45am local time (01:45 GMT).
Former Masters winner Schwartzel of South Africa birdied the first and saw Kiradech bogey the second to halve his lead.
Anders Hansen, Peter Lawrie, Edoardo Molinari, Padraig Harrington, Victor Dubuisson, Gregory Bourdy and China's Wu Ashun are a further shot back on nine-under-par at the $2.75 million co-sanctioned Asian Tour tournament.
Kiradech, dubbed Asia’s John Daly, is determined to close out the Malaysian Open after coming close three years ago when he entered the final round as the co-leader only to finish joint third.
“I’ve learned a lot from that. I’ve grown up in three years and I have learned a lot on how to play under pressure and how to play when you need to win. I think I have more experience and I hope it will help me tomorrow,” said the 23-year-old former world amateur champion.
World number three Luke Donald missed his first cut on the European Tour.
Englishman Donald saw his consistent streak end after posting rounds of 74 and 73 for a three over par total, three over the cut mark.
"I guess all good runs come to an end eventually. Hugely disappointed to miss my first ever cut in a European Tour event," Donald posted on his Twitter account.
The Briton was hopeful that the missed cut will have no bearing on his game when he tees up in search of his first major title at the US Masters in under three weeks' time.
"I've got a couple of weeks off to get ready for Augusta and I'll obviously be very diligent in my preparation," the 35-year old told the European Tour website.
"I would have loved to go back home in form, but in golf you just never know.
"We've seen it many times before when people go into tournaments with very little form and win - including Majors. So you just have to keep plugging and hope it's your turn."
Leading third and final round scores
-11: Kiradech APHIBARNRAT (THA) through 2 holes
-10: Charl SCHWARTZEL (RSA) through 2 holes
-9: Anders HANSEN (DEN) through 8 holes, Edoardo MOLINARI (ITA) through 5 holes, Padraig HARRINGTON (IRL) through 4 holes, Victor DUBUISSON through 4 holes, Gregory BOURDY (FRA) through 3 holes, WU Ashun (CHN) through 2 holes
-8: Jeev Milkha SINGH(IND) through 11 holes, Peter LAWRIE (IRL) through 6 holes, Jean GONNET (FRA) through 10 holes, Alastair FORSYTH (SCO) through 8 holes, Rafa CABRERA-BELLO (ESP) through 7 holes, Tommy FLEETWOOD (ENG)