We measured the electron density in an extreme ultra-violet (EUV) induced plasma. This is achieved in a low-pressure argon plasma by using a method called microwave cavity resonance spectroscopy. The measured electron density just after the EUV pulse is 2.6 × 1016 m-3. This is in good agreement with a theoretical prediction from photo-ionization, which yields a density of 4.5 × 1016 m-3. After the EUV pulse the density slightly increases due to electron impact ionization. The plasma (i.e. electron density) decays in tens of microseconds.