The winner will be given a free round-trip flight and lodging in Zurich.
In addition, the contest will benefit the Academy of Friends and the Breast Cancer Emergency Fund, with each organization receiving a Switzerland vacation package for two.
Heidi embodies the American view of Switzerland and, according to airline spokeswoman Jackie Pash, she is the ideal character to build awareness of the new flight options.
The airline has offered service between SFO and Zurich since June and will implement daily service in March.
"Both San Francisco and Switzerland are popular tourist destinations," Pash said. "Also, a lot of Swiss nationals live in San Francisco and there are a lot of connections and business opportunities between the two."
More than 25 participants will strut down the runway at 11 a.m. in Justin Herman Plaza at 1 Market St. in San Francisco.