Diffusion kurtosis imaging (DKI) is sensitive to tissue microstructure and may therefore be useful in the diagnosis and monitoring of disease in brain and body organs. Generally, diffusion magnetic resonance imaging (dMRI) in the body is challenging because of the heterogeneous body composition, which can cause image artefacts as a result of chemical shifts and susceptibility differences. In addition, the abdomen possesses physiological factors (e.g. breathing, heartbeat, blood flow) which may severely reduce image quality, especially when echo planar imaging is employed, as is typical in dMRI. Collectively, these challenging measurement conditions impede the use and exploration of DKI in the body. This impediment is further exacerbated by the traditionally large amount of data required for DKI and the low signal‐to‐noise ratio at the b‐values needed to effectively probe the kurtosis regime. Recently introduced fast DKI techniques reduce the challenge of DKI in the body by decreasing the data requirement substantially, so that, for example, triggering and breath‐hold techniques may be applied for the entire DKI acquisition without causing unfeasible scan times. One common pathological condition for which body DKI may be of immediate clinical value is kidney fibrosis, which causes progressive changes in organ microstructure. With its sensitivity to microstructure, DKI is an obvious candidate for a non‐invasive evaluation method. We present preclinical evidence indicating that the rapidly obtainable tensor‐derived mean kurtosis ( ) distinguishes moderately fibrotic kidneys from healthy controls. The presence and degree of fibrosis are confirmed by histology, which also indicates fibrosis as the main driver behind the DKI differences observed between groups. We therefore conclude that fast kurtosis is a likely candidate for an MRI‐based method for the detection and monitoring of renal fibrosis. We provide protocol recommendations for fast renal DKI in humans based on a b‐value optimisation performed using data acquired at 3 T in normal human kidney.