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Non-malleable secret sharing (NMSS) schemes, introduced by Goyal and Kumar (STOC 2018), ensure that a secret m can be distributed into shares m₁,⋯,m_n (for some n), such that any t (a parameter ≤ n) shares can be reconstructed to recover the secret m, any t-1 shares doesn't leak information about m and even if the shares that are used for reconstruction are tampered, it is guaranteed that the reconstruction of these tampered shares will either result in the original m or something independent of m. Since their introduction, non-malleable secret sharing schemes sparked a very impressive line of research. In this work, we introduce a feature of local reconstructability in NMSS, which allows reconstruction of any portion of a secret by reading just a few locations of the shares. This is a useful feature, especially when the secret is long or when the shares are stored in a distributed manner on a communication network. In this work, we give a compiler that takes in any non-malleable secret sharing scheme and compiles it into a locally reconstructable non-malleable secret sharing scheme. To secret share a message consisting of k blocks of length ρ each, our scheme would only require reading ρ + log k bits (in addition to a few more bits, whose quantity is independent of ρ and k) from each party’s share (of a reconstruction set) to locally reconstruct a single block of the message. We show an application of our locally reconstructable non-malleable secret sharing scheme to a computational non-malleable secure message transmission scheme in the pre-processing model, with an improved communication complexity, when transmitting multiple messages.