The discovery of superconducting nickelates provides a unique opportunity to explore the pairing mechanism of high-temperature superconductivity. Here, we use ultrafast terahertz spectroscopy to probe the temperature-dependent superfluid density in an infinite-layer samarium nickelate film with a T_c of 20 K. The superfluid density decreases linearly with rising temperature, consistent with clean-limit d-wave pairing in cuprate superconductors. From this linear relation, we extract a superconducting gap Δ(0) = 2.5 ± 0.1 meV and a gap-to-T_c ratio, 2∆(0) /k_B T_c≈3, suggesting that this sample lies in the weak-coupling regime. Furthermore, the ratio of the mean free path to the coherence length, l/ξ, is determined to be ~1.5, confirming clean-limit behavior. These findings suggest strong parallels between the pairing mechanisms in nickelate and cuprate superconductors.