Automatic Modulation Classification (AMC) is a vital component in the development of intelligent and adaptive transceivers for future wireless communication systems. Existing statistically-based blind modulation classification methods for Orthogonal Frequency Division Multiplexing (OFDM) often fail to achieve the required accuracy and performance. Consequently, the modulation classification research community has shifted its focus toward deep learning techniques, which demonstrate promising performance, but come with increased computational complexity. In this paper, we propose a lightweight subcarrier-based modulation classification method for OFDM systems. In the proposed approach, a selected set of subcarriers in an OFDM frame is classified first, followed by the prediction of the modulation types for the remaining subcarriers based on the initial results. A Lightweight Neural Network (LWNN) is employed to identify the initially selected set of subcarriers, and its output is fed into a Recurrent Neural Network (RNN) as an embedded vector to predict the modulation schemes of the remaining subcarriers in the OFDM frame.