We demonstrate that magnetic force microscopy is able to detect the superconducting state and to distinguish between the Meissner and Shubnikov phase of a high temperature superconductor. In the Meissner phase we observe an increasing, repulsive force with decreasing tip-to-sample distance. The force depends on the screening current density and therefore on the London penetration depth. Indeed, we detect a decrease in the maximum force as the temperature increases. In the Shubnikov phase a different behavior is observed. If the tip is approached staircase-like to a superconductor the repulsive force first increases and then decays rapidly. The superconductor has reacted to the increased stray field of the tip by readjusting the vortex structure to lower the total energy. The experiments are discussed in relation to existing theoretical predictions. We point out that magnetic force microscopy might become an important tool to directly observe the vortex structure and its complex phase transitions.