The officials refused to identify the player, pending a second test, but local media has reported that the top shutter tested positive for a banned substance at the world championships in Denmark in late August.
"One of our athletes in one major tournament has been found positive," Badminton Association of Malaysia deputy president Norza Zakaria told reporters after officials met for more than two hours to discuss the matter.
"We are very shocked, sad, and it is an earth-shattering news to us... We are hoping, keeping our fingers crossed that things will come to a positive conclusion at the end of the day."
Test results are expected within "one or two days", he said. He declined to give further details.
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Malaysia's sports minister had said on Tuesday that authorities were informed in an October 1 letter of the failed doping test.
Local media have since reported Lee failed the random test after the championship's semi-finals. He lost in the final to China's Chen Long.
Malaysians have expressed shock and disbelief over the allegations against Lee, one of only two prominent sports personalities in the country and a national icon.
Earlier this month, badminton was already hit with allegations of match fixing by two Danish players, who said they were approached by a Malaysian man via Facebook to throw matches.
Badminton officials Sunday condemned match fixing, saying they would work with authorities probing the matter.
It is also not the first doping scandal facing Malaysia recently.
On Saturday, two weightlifters were reportedly banned for two years for a doping offense in a local tournament in June.
Earlier this month, the head of the Wushu Federation of Malaysia resigned to take responsibility after Asian Games champion Tai Cheau Xuen tested positive for doping and was stripped of her gold medal.