The world's top-ranked player moved on with a 6-2, 6-7 (4), 1-0 victory when Osaka had to retire because of an abdominal injury.
It wasn't immediately clear when Osaka suffered the injury. She was in form during the tiebreaker, firing a service winner to convert her second set point under the warm sun at Aviva Centre.
Pliskova came out strong to open the third set and Osaka called for a trainer at the changeover. She briefly stretched out on the hardcourt before the decision was made.
The world's No. 50 player received treatment after the match and did not speak to reporters.
Second-seeded Simona Halep of Romania needed only 59 minutes to breeze by Barbora Strycova of the Czech Republic 6-1, 6-0, and American Sloane Stephens upset third-seeded German Angelique Kerber 6-2, 6-2.
Also, Caroline Garcia of France advanced with a 6-4, 6-2 win over American CiCi Bellis, and Lucie Safarova of the Czech Republic moved on with a 6-3, 6-7 (3), 6-2 victory over Ekaterina Makarova of Russia.
In doubles play, Ottawa's Gabriela Dabrowski and Latvia's Jelena Ostapenko defeated Germany's Julia Goerges and Ukraine's Olga Savchuk 4-6, 6-2, 10-3. The top-seeded doubles team of Makarova and Russia's Elena Vesnina beat Bianca Andreescu of Mississauga, Ontario, and Montreal-based Carson Branstine 6-1, 6-1.