Lee and Green both fired three-under-par 69s to be tied second after the first round of the $US2.6 million tournament in Calgary.
In-form American Lauren Coughlin set the pace with a 68 featuring five front-nine birdies at Shaunghessy Golf and Country Club on Thursday.
Minjee Lee is tracking nicely ahead of the Paris Olympics and is in contention at the Canadian Open. (AP PHOTO)
But Green and Lee are hot on her heels in a four-way share of second spot with Thailand's former world No.1 Ariya Jutanugarn and American major winner Jennifer Kupcho.
Dual major winner Lee was first in the clubhouse after mixing four birdies with her lone bogey on the par-5 fourth hole.
Kupcho had four birdies and a bogey.
"The weather was a bit crazy," Kupcho said. "I feel like we had three different seasons in 18 holes. Definitely got sunny at the end and that's when I made all my birdies. Really, just tried to stay patient all day."
World No.6 Green then produced a putting masterclass to join her fellow West Australian at three under.
Chasing a third win of an already exceptional year, Green rolled in six one-putts on the back nine, her best a double-breaking long-range effort for birdie on the 14th.
"It was difficult out there," Green said. "It's nice that the sun has peeped out. It was pretty cold towards the middle of our round. Just super happy to finish under par this afternoon."
New Zealand's three-time champion Lydia Ko produced the only bogey-free round of the day, a two-under 70 to be one stroke further back in joint sixth with South Koreans Haeran Ryu, Jenny Shin and Hye-Jin Choi.
Like Lee, Ko is also heading to her third Games next week, hoping to strike gold after picking up the silver medal in Rio de Janeiro in 2016 and bronze in Tokyo three years ago.
"It would be pretty cool," said the former world No.1 who needs one more tour victory to be elevated into women's golf's Hall of Fame.
"Going into Rio, I really wanted to medal and coming off with a silver medal I think it was the best second place I've ever had.
"And it was the same for Tokyo.
"If I do win gold at Paris, I feel like somebody needs to get me like a Cinderella slipper because it's just a story that even I couldn't have drawn up.
"So, yeah, very excited for Paris in a couple of weeks and we've got our last major at St Andrews at the home of golf, so a lot of golf left."
But Coughlin, fourth last start at the Evian Championship in France after leading for much of the final round, is again the player to catch.
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