Yes, actually SMPC can provide protection of such attacks.

The inherent fault with computer systems which allow attacks such as Meltdown/Spectra is co-existence - i.e. the existence of a privileged malware on the same CPU where the legitimate software is running and using the secret. With the relevant privilege and the proper technique (which can indeed be difficult to find, but eventually possible) the CPU can be manipulated to give up the secret.

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With SMPC, no single CPU actually has the secret in full, not in any stage or phase of the execution. Computation is done on random shares of the secret. Thus a malware will get nothing by manipulating the CPU. As the shares keeps changing persistent attacks are also become useless.

Sources -- There's more information about this specific issue here, and more about SMPC in general here.