When a magnetic impurity exists in a metal, conduction electrons form a spin cloud that screens the impurity spin. This basic phenomenon is called the Kondo effect(1,2). Unlike electric-charge screening, the spin-screening cloud(3-6) occurs quantum coherently, forming spin-singlet entanglement with the impurity. Although the spins interact locally around the impurity, the Kondo cloud can theoretically spread out over several micrometres. The cloud has not so far been detected, and so its physical existence-a fundamental aspect of the Kondo effect-remains controversial(7,8). Here we present experimental evidence of a Kondo cloud extending over a length of micrometres, comparable to the theoretical length xi(K). In our device, a Kondo impurity is formed in a quantum dot(2,9-11), coupling on one side to a quasi-one-dimensional channel(12) that houses a Fabry-Perot interferometer of various gate-defined lengths L exceeding one micrometre. When we sweep a voltage on the interferometer end gate-separated by L from the quantum dot-to induce Fabry-Perot oscillations in conductance we observe oscillations in the measured Kondo temperature T-K, which is a signature of the Kondo cloud at distance L. When L is less than xi(K) the T-K oscillation amplitude becomes larger as L becomes smaller, obeying a scaling function of a single parameter L/xi(K), whereas when L is greater than xi(K) the oscillation is much weaker. Our results reveal that xi(K) is the only length parameter associated with the Kondo effect, and that the cloud lies mostly within a length of xi(K). Our experimental method offers a way of detecting the spatial distribution of exotic non-Fermi liquids formed by multiple magnetic impurities or multiple screening channels(13-16) and of studying spin-correlated systems.