The greenback hit a two-week high against a basket of major rivals after the Fed raised interest rates and signaled four more hikes are to come next year.
Depressed oil prices in the face of a relentless build in oversupply added to pressure on the Canadian dollar.
US crude prices were down 0.25 percent to $35.43 a barrel, while Brent crude added 0.83 percent to $37.70.
At 9:28 a.m. EST (1428 GMT), the Canadian dollar was trading at C$1.3876 to the greenback, or 72.07 US cents, weaker than the Bank of Canada's official close of C$1.3785, or 72.54 US cents.
The currency's strongest level of the session was C$1.3778, while it hit its weakest level since June 2004 at C$1.3880.
The number of Americans filing for unemployment benefits last week fell from a five-month high, suggesting sustained labor market healing that could support further Fed tightening.
Canadian government bond prices were mixed across the maturity curve, with the two-year price down 0.5 Canadian cent to yield 0.552 percent and the benchmark 10-year rising 41 Canadian cents to yield 1.466 percent.
The curve flattened in sympathy with US Treasuries, as the spread between the 2-year and 10-year yields narrowed by 4.5 basis points to 91.4 basis points, indicating outperformance for longer-dated maturities.
Canadian inflation data for November is awaited on Friday. A Reuters poll shows a pickup in the consumer price index to a 1.5 percent pace from a year earlier.