We report a detailed investigation on the lower critical field H{c1} of the superconducting Ba0.6K0.4Fe2As2 (122) single crystals. A pronounced kink is observed on the H{c1}(T) curve, which is attributed to the existence of two superconducting gaps. By fitting the data H{c1}(T) to the two-gap BCS model in the full temperature region, a small gap of Delta{a}(0)=2.0+/-0.3 meV and a large gap of Delta{b}(0)=8.9+/-0.4 meV are obtained. The in-plane penetration depth lambda{ab}(0) is estimated to be 105 nm corresponding to a rather large superfluid density, which points to the breakdown of the Uemura plot in 122 superconductors.