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Searching for an ideal magnetic Weyl semimetal hosting only a single pair of Weyl points has been a focal point for systematic clarification of its unique magnetotransport derived from the interplay between topology and magnetization. Among the candidates, triangular-lattice antiferromagnet EuCd$_2$As$_2$ has been attracting special attention due to the prediction of the ideal Weyl semimetal phase in the ferromagnetic state, however, transport properties of low-carrier density samples have remained elusive. Here we report molecular beam epitaxy growth of EuCd$_2$As$_2$ films, achieving low-hole density in the range of $10^{15}$-$10^{16}$ cm$^{-3}$ at low temperature. Transport measurements of such low-carrier density films reveal an insulating behavior with an activation gap of about 200 meV, which persists even in the field-induced ferromagnetic state. Our work provides an important experimental clue that EuCd$_2$As$_2$ is intrinsically insulating, contrary to the previous prediction.