Scotland's Eve Muirhead opened the defence of her title against the Swiss, led by Mirjam Ott, but despite a strong start the Scots were eventually edged out in Karlstad, Sweden.
After taking a 1-0 lead following the second end in the Group A clash, Scotland were 3-2 up past the half-way stage but failed to score in the final four ends.
The Swiss won 2-0 in the eighth to go 4-3 ahead leaving Muirhead needing to spin out a Swiss stone and score two to win in the tenth. But she ended giving a single steal to lose the match 5-3.
"It was a tough shot for the two," she admitted afterwards. "It's always difficult to settle for just the one when you have got a chance of a win.
"Looking at the way it spun, now I'm not so sure it was on."
Scotland's men, led by Tom Brewster, also opened with defeat as the World Championship runners-up were beaten 6-5 by the Czech Republic in Group A.
The Scots won the penultimate end 2-0 to draw level at 5-5 only to lose 1-0 in the tenth.
Later, they bounced back with a 7-2 win over Germany to get their campaign up and running.
Meanwhile, in Group B England's men were beaten 7-5 by Italy despite a brave attempt at a comeback.
Italy roared into a 4-0 lead by the fourth end, but England responded and were back to 6-3 behind at the end of the sixth.
England won the last two ends 1-0 but required more having fallen further behind in the seventh.
The English women's team, led by Fiona Hawker, started Group B in fine fashion with a 6-4 win over Estonia, only to be beaten 11-4 by Austria in their second outing.