While Olympic bronze medallist Saina went down narrowly to lower-ranked Yao Xue of China 21-16, 10-21, 19-21 in 56 minutes, Sindhu was beaten by sixth seed Yeon Ju Bae of Korea 16-21, 19-21 in 45 minutes at the Putra Stadium.
World No 8 Saina lived up to her billing in the first game, winning it comfortably despite the scores running neck and neck, till 12-all.
But the Indian ace was in for a surprise in the second as the Chinese world No 25 went on all all-out attack and raced away to take the game level the scores 1-1.
Saina started off well in the decider and appeared to have things under control as she led 7-4 and 10-8. However, Xue drew abreast at 10 and from then called the shots to open up an 18-14 lead.
The Indian fought back and scored three successive points to reduce the deficit to 17-18 before catching up at 19-all.
But the Chinese raised her game when it mattered most and bagged two quick points to stun her fancied opponent.
Meanwhile, World Championship bronze-medallist Sindhu got off to a fine start, opening up a 2-0 lead before extending it to 6-3. But the World No. 7 Korean settled down and drew abreast at six and surged to 10-6 by winning seven points on the trot.
Sindhu fought her way back to reduce the margin to 9-10 only to see the higher ranked Korean regain the lead at 14-13 and proceed to take the first game.
In the second game, too, the Korean came from behind after Sindhu led 9-6, 19-15. Just when the World No. 11 Indian looked set to seal the second game and take the match to the decider, Bae scored four straight points to make it 19-all and took the next two points to clinch victory.
Image: Bae Yeon Ju of South Korea celebrates after beating India's P V Sindhu during Day 3 of the Malaysia Super Series in Kuala Lumpur, Malaysia.
Photograph: Stanley Chou/Getty Images
Saina to skip few tournaments to focus on fitness
Sindhu the new star as Saina endures title drought
The Top 10 Sporting Breakthroughs in 2013
Saina, Sindhu advance in Malaysia Open
Posco steel plant to be operational soon: PM