Kirk Woodman was abducted by gunmen on Tuesday night from a mine near the country's border with Niger.
Canada's Foreign Minister Chrystia Freeland condemned those responsible "for this terrible crime".
Mr Woodman was the second Canadian to go missing in Burkina Faso in recent weeks.
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Authorities are investigating a link between the discovery of two suspected MH370 fragments that washed up on Madagascar and the assassination of a Malaysian diplomat.