Canada batted first in New Williamfield and posted 133 for three in a match reduced to 13 overs a side. Nitish Kumar led the way with 52 off 25 balls, with Navneet Dhaliwal adding 28 for Canada.
Oman reached its winning target at 135 for three with 10 balls to spare for an eight-wicket victory on the Duckworth-Lewis Method.
Canada dropped to 0-2-0 while Oman improved to 1-1-0 at the 14-team tournament that runs through July 26 in Scotland and Ireland.
The top six sides will join the ICC's 10 full members for the ICC World Twenty20 India 2016, which runs March 11 to April 3.
Canada is in Group B with Afghanistan, United Arab Emirates, Netherlands, Oman, Scotland and Kenya.
Canada's next game is Tuesday against the United Arab Emirates (0-3-0).