Kass grew up in Paide. She had already received recognition by the time she was discovered at age 14 in a Tallinn supermarket by an Italian modeling scout. Kass had wanted to compete for the Miss Estonia title, but the offer to fly to Milan to start a modeling career seemed like a more glamorous and lucrative option.

Kass moved to Paris at the age of 18. She received exposure on the cover of magazines worldwide, such as L'Officiel and Vogue (France) in 1997, ELLE (Australia), Image (UK), Madame Figaro, Numéro France, Vogue (France), and Vogue (US) in 1999.

In 1999, Kass modeled for top designers such as Alberta Ferretti, Anna Sui, BCBG, Bill Blass, Calvin Klein, Chanel, Christian Dior, DKNY, Dolce & Gabbana, Gianfranco Ferré, Gianni Versace, Gucci, Jill Stuart, MaxMara, Michael Kors, Moschino, Nicole Miller, Prada, Oscar de la Renta, Ralph Lauren, Tommy Hilfiger, Louis Vuitton, and Valentino. Kass has posed in advertisements for Calvin Klein, Chanel, Donna Karan, General Motors Corporation, Guy Laroche, Krizia, and Versace. She is also recognized for her appearances in a The Gap denim advertising campaign. Kass is a spokesperson for Sephora, one of the world's leading cosmetics retailers, and the Christian Dior perfume, J'adore.

Kass was recognized by Vogue as "Model of the Year" at the 2000 VH1/Vogue Fashion Awards.

Kass is well-known for her distinctive runway walk. A quirk of the Estonian supermodel is that while she is very tall, her feet are quite small (about an American size seven). It is said that she sometimes simply falls out of her shoes while walking.

In 2004, Kass starred in the Estonian murder-mystery film Täna öösel me ei maga (We Won't Sleep Tonight). The international release was retitled Set Point.