I'm guessing you're exporting from Maya? (It helps to indicate the app and version) Did you try the advice in the Unity help docs? https://docs.unity3d.com/2018.1/Documentation/Manual/HOWTO-exportFBX.html#Maya https://docs.unity3d.com/Manual/HOWTO-ImportObjectsFrom3DApps.html#Maya
you can narrow it down .. fbx has supported blendshapes for a long, long time so version shouldn't be a problem provided the exporter has the correct options ticked (i.e the export blendshapes option) reimport the exported file to maya (being careful to make sure you include all the appropriate options) - if the meshes are…