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 effect1,2. Unlike electric-charge screening, the spin-screening cloud3-6 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 controversial7,8. Here we present experimental evidence of a Kondo cloud extending over a length of micrometres, comparable to the theoretical length ξK. In our device, a Kondo impurity is formed in a quantum dot2,9-11, coupling on one side to a quasi-one-dimensional channel12 that houses a Fabry-Pérot 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-Pérot oscillations in conductance we observe oscillations in the measured Kondo temperature TK, which is a signature of the Kondo cloud at distance L. When L is less than ξK the TK oscillation amplitude becomes larger as L becomes smaller, obeying a scaling function of a single parameter L/ξK, whereas when L is greater than ξK the oscillation is much weaker. Our results reveal that ξK is the only length parameter associated with the Kondo effect, and that the cloud lies mostly within a length of ξK. Our experimental method offers a way of detecting the spatial distribution of exotic non-Fermi liquids formed by multiple magnetic impurities or multiple screening channels13-16 and of studying spin-correlated systems.