Half points were awarded because only 32 of the scheduled 56 laps had been completed.
The race was red-flagged when a torrential downpour, with thunderclaps and lightning streaking across the darkened Sepang skies, made driving conditions impossible even behind the safety car.
Button, the championship leader who had again started from pole position after a Brawn one-two in the Australian season-opener last weekend, was leading behind the safety car when officials called a halt.
The Briton, who won in Melbourne [ Images ] with the safety car pitting only on the final corner, had already made four pitstops in the changing conditions.
"What a crazy race, it really was," said the 29-year-old after some slippery podium celebrations. "I still haven't seen the chequered flag (this season) without the safety car in front.
"It was really bad conditions, you couldn't actually see the circuit," added Button.
Germany's [ Images ] Nick Heidfeld [ Images ] was second for BMW-Sauber with compatriot Timo Glock [ Images ] third for Toyota [ Images ] with the results based on the positions at the end of the penultimate lap.
It was only the fifth time in F1 history that half points had been awarded in a race.
"The visibility is nothing. With the amount of water on the track, it is now really dangerous," Renault's [ Images ] double world champion Fernando Alonso [ Images ] told BBC television while waiting for a possible re-start in the fading light.
"They were the most dangerous conditions I've ever been in for sure," said Hamilton.
Champions Ferrari [ Images ] failed to score their first point of the season, with Brazilian Felipe Massa [ Images ] ninth and 2007 champion Kimi Raikkonen [ Images ] 14th after changing to full wet tyres too early and paying the price.
There was confusion after the race was abandoned, with drivers awaiting the unlikely chance of a re-start while the clock ticked towards the two-hour limit and the daylight faded.
With Glock ahead of Heidfeld at the red flag, there was also uncertainty about the final podium positions.
The last race to be abandoned due to heavy rain was Australia [ Images ] in 1991 when the grand prix was halted after 14 of the 81 scheduled laps. Others have been cut short by accidents or re-started.