The necessity of using a fixed-size word vocabulary in order to control the model complexity in state-of-the-art neural machine translation (NMT) systems is an important bottleneck on performance, especially for morphologically rich languages. Conventional methods that aim to overcome this problem by using sub-word or character-level representations solely rely on statistics and disregard the linguistic properties of words, which leads to interruptions in the word structure and causes semantic and syntactic losses. In this paper, we propose a new vocabulary reduction method for NMT, which can reduce the vocabulary of a given input corpus at any rate while also considering the morphological properties of the language. Our method is based on unsupervised morphology learning and can be, in principle, used for pre-processing any language pair. We also present an alternative word segmentation method based on supervised morphological analysis, which aids us in measuring the accuracy of our model. We evaluate our method in Turkish-to-English NMT task where the input language is morphologically rich and agglutinative. We analyze different representation methods in terms of translation accuracy as well as the semantic and syntactic properties of the generated output. Our method obtains a significant improvement of 2.3 BLEU points over the conventional vocabulary reduction technique, showing that it can provide better accuracy in open vocabulary translation of morphologically rich languages.