We present adaptive optics-assisted J- and K-band integral field spectroscopy of the inner 300 x 300 pc of the Seyfert 2 galaxy NGC1068. The data were obtained with the Gemini NIFS integral field unit spectrometer, which provided us with high-spatial and -spectral resolution sampling. The wavelength range covered by the observations allowed us to study the [CaVIII], [SiVI], [SiVII], [AlIX] and [SIX] coronal-line (CL) emission, covering ionization potentials up to 328 eV. The observations reveal very rich and complex structures, both in terms of velocity fields and emission-line ratios. The CL emission is elongated along the NE-SW direction, with the stronger emission preferentially localized to the NE of the nucleus. CLs are emitted by gas covering a wide range of velocities, with maximum blueshifts/redshifts of ~ -1600/1000 km/s. There is a trend for the gas located on the NE side of the nucleus to be blueshifted while the gas located towards the SW is redshifted. The morphology and the kinematics of the near-infrared CLs are in very good agreement with the ones displayed by low-ionization lines and optical CLs, suggesting a common origin. The line flux distributions, velocity maps, ionization structure (traced by the [SiVII]/[SiVI] emission-line ratio) and low ionization emission-line ratios (i.e., [FeII]/Pabeta and [FeII]/[PII]) suggest that the radio jet plays an important role in the structure of the coronal line region of this object, and possibly in its kinematics.