Canadian wholesale trade fell 0.5 percent due to lower sales in the personal and household goods sector, Statistics Canada said. Analysts surveyed by Reuters had forecast a 0.4 percent increase.
The data "bodes poorly" for growth in the economy in December, Ryan Brecht, a senior economist at Action Economics, said in a research note.
On Friday, data showed that Canadian manufacturing shipments also declined in December.
The US dollar climbed on Tuesday against a basket of major currencies, continuing a rebound from a sharp decline in recent weeks that took it to three-year lows.
At 9:19 a.m. EST (1419 GMT), the Canadian dollar was trading 0.4 percent lower at C$1.2604 to the greenback, or 79.34 US cents.
The currency's strongest level of the session was C$1.2558, while it touched its weakest since Feb. 14 at C$1.2629. Global stocks fell as Wall Street returned from a long holiday weekend, pressured by a rise in bond yields.
Lower equity markets tend to weigh on commodity-linked currencies, such as the Canadian dollar.
Reduced supply from Canada to the United States caused by pipeline reductions helped boost US crude oil prices. US crude prices were up 0.2 percent at $61.81 a barrel.