The study explored the contribution of two aspects of inflectional morphological awareness, verb inflection and noun–adjective inflection, to word reading and reading comprehension in the Greek language, which is an orthographically transparent language. Participants (120 first graders, 123 second graders, 126 third graders) were given two oral language experimental tasks of inflectional morphological awareness. Furthermore, phonological awareness, receptive vocabulary, expressive vocabulary, decoding, and reading comprehension were evaluated. It was revealed that noun–adjective inflectional morphology contributed significantly to decoding only in first grade, while verb inflectional morphology had a significant contribution to reading comprehension in third grade. It is interesting that inflectional morphological awareness did not predict reading skills for second graders. Phonological awareness was a firm predictor of word reading in all grades and made a unique contribution in Grades 2 and 3. Finally, in all grades, receptive vocabulary was a steady predictor of reading comprehension, whereas expressive vocabulary predicted only first-grade reading comprehension. It is suggested that inflectional morphological awareness may be an important predictor of early reading in a language with a shallow orthography and a rich morphology.