Directional SiC/Cu–Si composite with co-continuous microstructure was fabricated via spontaneous infiltration of Cu-24at%Si alloy into a directional porous SiC ceramic produced by a high temperature recrystallization process. The initial continuous microstructure of the directional porous SiC ceramic after spontaneous infiltration can be maintained and the as-fabricated SiC/Cu–Si composite exhibits significant thermo-physical anisotropy, with higher thermal conductivity (TC) and lower coefficients of thermal expansion (CTE) in the axial direction. Furthermore, the extent of TC anisotropy can also be significantly affected by the test temperature besides microstructural anisotropy. The higher the test temperature is, the lesser the anisotropy degree of TC becomes. This can be attributed to the varying TC ratio of the SiC to the Cu–Si alloy with increased temperature. In contrast, the temperature has minor effect on the anisotropy of CTE.