I understand you are confused, because the electron's potential (EM) energy is negative. When you say becomes higher, you mean less negative.
Let's say the electron is at a stable energy level around the nucleus as per QM. This is due to certain forces:
the EM force (potential negative energy) keeps the electron close to the nucleus
the kinetic energy of the electron keeps the electron away from the nucleus
the HUP keeps the electron away from the nucleus (in case it would get too close)
Now these three forces equal out, and the electron is in a stable QM orbit (not classical orbital).
Now let's say the electron/atom absorbs a photon. The photon's energy gets transferred into the electron, and the electron moves further from the nucleus.
Now let's see the forces away from the nucleus:
the EM force (attraction) between the electron and the nucleus becomes less strong, the potential negative energy decreases, which means higher energy
the kinetic energy of the electron must decrease, less momentum
the HUP becomes less important
So basically the answer to your question is, away from the nucleus, the electron's potential (EM) negative energy decreases, which means higher energy.