Is there a minimum period I must have lived in Canada before departure tax applies when I leave?

Yes. If you were resident in Canada for only a short period before you left, a specific exemption can remove certain property from the departure-tax deemed disposition altogether, rather than requiring you to value and report gains on it the way a longer-term resident would. The exemption is generally aimed at property you owned before you became a Canadian resident, or that you received by inheritance or gift while you were resident here, recognizing that Canada didn't really have much claim to tax the growth in that property in the first place.

Whether you qualify turns on how long you were actually resident in Canada during a set look-back period, so this isn't available to everyone who leaves — someone who lived in Canada for many years doesn't get this exemption just because they're now moving on. It's specifically aimed at people whose Canadian residency was genuinely temporary.

If you think you might qualify, confirming your residency history against the exemption's requirements before you file your departure-year return is important, since claiming it incorrectly, or missing it when you do qualify, both create problems worth avoiding with proper advice.