This depends on the market you are interested in pursuing. For high fashion runway modelling (what you see on Fashion Television), yes there is a height requirement however, there are always exceptions to the rule. For example, Kate Moss is 5’6” and there are numerous other female models that fall below the high fashion height standards set by designers for the runway.
There is no height requirement for children, tweens or young teens. There is also no height requirement for commercial print modelling, acting (TV commercials, television, film, etc…) or in local / national mall fashion shows who are looking to appeal to the everyday shopper & select models in all shapes & sizes.