Saina lost 8-21, 21-18, 19-21 in a match which lasted more than one hour.
The 26-year-old Indian surrendered the first game easily but gave a tough fight in the second and third.
In the first game, the Indian shuttler started off on a poor note. She at one point gave away eight consecutive points to surrender the initiative.
In second game, Saina regained her calm and matched the pace at which her opponent was playing. As a result, after trailing initially, she bounced back in style to turn the flow of the proceedings.
The third game saw some errors committed by the Hyderabadi shuttler but despite those, Saina, who was trailing by seven points (11-18), played some good shots to pull level at 18-18.
But Cheung proved superior during the crunch period of the contest and clinched the match 21-19.
She will now take on P.V. Sindhu in the semi-final, who defeated Xiaoyu Liang of Singapore in quarters. Had Saina won the match, she would have faced her compatriot Sindhu in the last four stage.
The Olympic silver medallist faced a tough challenge at the Hong Kong Coliseum before scripting a 21-17, 21-23, 21-18 win in one hour and 19 minutes.
Sindhu was off to a difficult start with Liang taking the lead in the early stages of the opening game.
She trailed by three points at one stage but pulled level at 8-8.
A run of four consecutive points saw her take a 14-10 lead and the Indian never looked back from there, going on to take the first game.
The second game was a bitterly fought affair. Liang again enjoyed a better start, taking a 3-0 lead but Sindhu soon restored parity.
The lead changed hands several times with the Indian taking a 16-12 lead at one stage following a four-point streak.
Liang equalised at 18-18 which set up a tense finish. With both shuttlers locked at 21-21, the Singaporean took a couple of back-to-back points to take the second game and level the scores.
Sindhu was in trouble in the third set as well with her opponent leading 14-7 at one stage. But the Hyderabad shuttler staged a superb fightback to win six back to back points and draw level at 15-15.
With the momentum firmly behind her, Sindhu continued her resurgence to clinch the game and the match.