Czech Pliskova, playing her first tournament with the top ranking, was pushed into a deciding set by qualifier Osaka before the 19-year-old called for the trainer when trailing 6-2 6-7(4) 1-0 and promptly withdrew.
"She played well, especially in the second set she was fighting pretty hard, much better than the first," said Pliskova.
"I was just trying to stay in the game, the first game of the third set was very tough I didn't even know she was injured."
Pliskova, playing her first tournament since a shock second round defeat at Wimbledon, had shown signs of rust in a ragged opening win over Anastasia Pavlyuchenkova but looked more like a world number one as she swept four straight games to take the first set from 50th-ranked Osaka.
But the Japanese rallied to match the lanky Czech shot-for-shot in a gripping second set, then dominated the tiebreak.
During the changeover, Osaka told her coach that she was feeling discomfort and was told to withdraw if the pain persisted to avoid the risk of further injury.
Osaka did just that, calling for the trainer after dropping serve to open the third set.
"I think my game today was much better, especially my serve," said Pliskova, who clubbed 13 aces. "I didn't lose my serve in this match today, I'm happy with the way I was serving today."
Pliskova will need to have her serve firing on all cylinders when she meets sixth seed and former world number one Caroline Wozniacki in the last eight.
In a battle of former-Rogers Cup champions, a ruthless Wozniacki showed no mercy by sweeping past her good friend Agnieszka Radwanska 6-3 6-1 in just 78 minutes.
The only hiccup in an otherwise polished effort against the 10th-seeded Pole came when Wozniacki was up 5-0 in the second and squandered three match points.
But the Dane closed out the match on the next chance with a stinging forehand winner.
"We've known each other since we were five and six years old so there are no secrets out there," said Wozniacki, who has reached five finals this season without winning a title.
"It is always unfortunate to play a good friend in such an early round but at the same time it is part of the game."
Czech Lucie Safarova also made the last eight by outlasting Russia's Ekaterina Makarova 6-3 6-7(3) 6-2, while France's Caroline Garcia beat 18-year-old American Catherine Bellis 6-4 6-2.
Ukraine's Elina Svitolina broke American Venus Williams six times en route to a near-perfect 6-2 6-1 victory.
Svitolina's 40th win of the year booked her first Rogers Cup quarter-final appearance.
Unseeded American Sloane Stephens upset former world number one Angelique Kerber 6-2 6-2 on Thursday as she continues her comeback from a year-long absence due to a foot injury.
Stephens will face Czech Lucie Safarova in the quarter-finals.
Fourth seed Garbine Muguruza dispatched Ashleigh Barty of Australia 6-0 3-6 6-2 at their centre court meeting.
(Additional reporting by Rory Carroll in Los Angeles; Editing by Ken Ferris/Ian Ransom)
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