The Type IIb supernova (SN) 2011dh exploded in the nearby galaxy M51 (the Whirlpool galaxy) and provides us with one of the best laboratories to study early high-energy emission from SNe. We give here a comprehensive view of the X-ray properties of SN 2011dh from the analyses of two pointed XMM–Newton early observations as well as the full Swift X-ray Telescope (XRT) data set (163 ks). Due to the high XMM–Newton throughput, we were able to satisfactorily fit the X-ray spectrum with two hot diffuse gas components including an additional absorption component to our Galaxy. A power-law model provided a worse description of the data. In addition, the early Swift XRT light curve hints of a flux excess at early times (≲3 d), consistent with the adiabatic cooling of stellar’s photosphere a few days after the shock breakout.