Context. Ionization plays a central role in the gas-phase chemistry of molecular clouds. Since ions are coupled with the magnetic fields, which can in turn counteract the gravitational collapse, it is of paramount importance to measure their abundance in star-forming regions. Aims. We use spectral line observations of the high-mass star-forming region NGC 6334 I to derive the abundance of two of the most abundant molecular ions, HCO+ and N2H+, and consequently, the cosmic ray ionization rate. In addition, the line profiles provide information about the kinematics of this region. Methods. We present high-resolution spectral line observations conducted with the HIFI instrument on board the Herschel Space Observatory of the rotational transitions with Jup > 5 of the molecular species C17O, C18O, HCO+, H13CO+, and N2H+. Results. The line profiles display a redshifted asymmetry consistent with a region of expanding gas. We identify two emission components in the spectra, each with a different excitation, associated with the envelope of NGC 6334 I. The physical parameters obtained for the envelope are in agreement with previous models of the radial structure of NGC 6334 I based on submillimeter continuum observations. Based on our new Herschel/HIFI observations, combined with the predictions from a chemical model, we derive a cosmic ray ionization rate that is an order of magnitude higher than the canonical value of 10^(-17) s-1. Conclusions. We detect an expansion of the envelope surrounding the hot core of NGC 6334 I, which is mainly driven by thermal pressure from the hot ionized gas in the region. The ionization rate is dominated by cosmic rays originating from outside the source, although X-ray emission from the NGC 6334 I core could contribute to the ionization in the inner part of the envelope.