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This letter reports the first demonstration of a monolithic heterostructure with a large electric tuning of the ferromagnetic resonance (FMR) at millimeter-wave frequencies. The structure is composed of a barium-strontium-titanate (BST) film and two thin platinum electrodes, all grown on a barium ferrite slab with in-plane uniaxial anisotropy. The electric tuning of the FMR responses around 60 GHz was obtained for bias voltages across the BST layer in the 0-30 V range. The average tuning rate was 1.1 MHz/V. The highest incremental response was 2.1 MHz/V. These rates are significantly higher than the previously reported values for nonmonolithic structures.