Germany, winners of the last two World Cups and strong favourites this time around too, got their campaign off to the perfect start when Kerstin Garefrekes headed home after 10 minutes.
Canada looked good though with striker Christine Sinclair causing the German defence problems. But it was Germany who scored the next goal when midfielder Celia Okoyino da Mbabi broke through and slotted the ball past Erin McLeod.
The Canadians did pull one back late on thanks to a stunning 25-yard free-kick from Sinclair, but despite a tense finale, the Germans held on.
In the earlier game, France striker Marie-Laure Delie scored the first goal of the tournament in a scrappy goal-mouth scramble, controlling a low cross and stabbing the ball home for the victory. With the win France join Germany at the top of Group A.
The 32-match tournament, comprising four groups of four teams, will be played at nine venues across Germany, with the group winners and runners-up progressing to the quarter-finals, ending with the final in Frankfurt on 17 July.
More than 700,000 tickets have been sold for the three-week event, with about half the games expected to attract more than 20,000 fans.
The United States, take on North Korea, Colombia and Sweden in Group C with their first game Tuesday.