When a second-order magnetic phase transition is tuned to zero temperature by a nonthermal parameter, quantum fluctuations are critically enhanced, often leading to the emergence of unconventional superconductivity. In these "quantum critical" superconductors it has been widely reported that the normal-state properties above the superconducting transition temperature T(c) often exhibit anomalous non-Fermi liquid behaviors and enhanced electron correlations. However, the effect of these strong critical fluctuations on the superconducting condensate below T(c) is less well established. Here we report measurements of the magnetic penetration depth in heavy-fermion, iron-pnictide, and organic superconductors located close to antiferromagnetic quantum critical points, showing that the superfluid density in these nodal superconductors universally exhibits, unlike the expected T-linear dependence, an anomalous 3/2 power-law temperature dependence over a wide temperature range. We propose that this noninteger power law can be explained if a strong renormalization of effective Fermi velocity due to quantum fluctuations occurs only for momenta k close to the nodes in the superconducting energy gap Δ(k). We suggest that such "nodal criticality" may have an impact on low-energy properties of quantum critical superconductors.