"Canada was one of the strongest opponents we could have drawn, not only for the quality of the team led by Milos Raonic but also for the fact that we are the away team and only a week after the Australian Open," Spain captain Alex Corretja said.
"That means another long journey and all the effects of the change in time zone.
"It will be a tough tie but the important thing right now is to focus on the final we have to play in two months against Czech Republic," he told the Spanish tennis federation (RFET) website (www.rfet.es).
Top seeds Spain have met Canada once before, at the same stage of the competition in 1991 when they won in Murcia.
The Czechs, who host Spain in this year's final from Nov. 16-18, begin next year's world group campaign in Switzerland.
They boast a 6-2 head-to-head record against the Swiss but lost to them the last time they played in Switzerland, in 1998.
This year's losing semi-finalists, the United States and Argentina, will start the 2013 campaign at home, with the Americans taking on Brazil and the Argentines facing Germany.
Arnaud Clement's first tie as France captain since he took over from Guy Forget will be at home to Israel. The French have not lost to the Israelis in three meetings.
Kazakhstan, who won a playoff with Uzbekistan to retain their world-group status, begin next year's competition by welcoming Austria, while Italy host Croatia.
Serbia, Davis Cup champions in 2010, travel to Belgium.
The ties will be played from February 1 to 3.
World group draw (home teams first):
Canada v Spain
Italy v Croatia
Belgium v Serbia
U.S. v Brazil
France v Israel
Argentina v Germany
Kazakhstan v Austria
Switzerland v Czech Republic