Nanocellulose reinforced foams are lightweight with improved mechanical properties; however, the strain‐rate effect on their mechanical response is not yet fully understood. In this work, rigid polyurethane foams (PUFs) nanostructured with bacterial nanocellulose at 0.2 wt % (BNCF) and without it (PUF) are synthesized and subjected to compression tests at different strain rates. The BNC acts as a nucleation agent, reducing the cell size but maintaining a similar apparent density of 40.4 ± 3.3 kg m−3. Both BNCF and PUF exhibit strain‐rate effect on yield stress and densification strain. The BNCF exhibits localized progressive crushing and reduced friability, causing a remarkable recovery in the transverse direction. Numerical simulations show that functionally graded foams subjected to impact could be designed using different layers of PUF and BNCF to vary energy absorption and acceleration rate. The results presented herein warrant further research of the mechanical properties of nanostructured foams for impact applications. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 137, 48701.