If you are referring to female runway models for the major fashion houses, the minimum height is 5'8", but most models are more likely 5'10" to 6'. In the fashion industry anyone shorter than 5'9" is called petite; petite clothing is intended for women under 5'4". Advertising for petite models is a likely scam. It helps to have an ectomorphic body type― tall and thin with difficulty gaining weight. In the picture below the woman on the left is an ectomorph.

http://s3.media.squarespace.com/producti...

The rest of these links give more complete info about different types of models. One can also model for retail ads and catalogs without needing exceptional height, but you are unlikely to get rich or famous.

http://models.com/help/005-what_are_requ...

http://www.newmodels.com/height.html

http://www.wolfkettler.co.uk/models/pro-...

5-8in