In this paper, we present the Noether symmetries of a class of the Bianchi type I anisotropic model in the context of f(T) gravity. By solving the system of equations obtained from the Noether symmetry condition, we obtain the form of f(T) as a teleparallel form. This analysis shows that teleparallel gravity has the maximum number of Noether symmetries. We derive the symmetry generators and show that there are five kinds of symmetries, including time and scale invariance under metric coefficients. We classify the symmetries and we obtain the corresponding invariants.