  We have studied the phase diagram of MgB$_2$ superconductor using a single
crystal for ${\bf H}\parallel c$-axis. For the first time we report the
existence of peak effect in the screening current in MgB$_{2}$ single crystal
for ${\bf H}\parallel c$-axis. In the magnetic field regime $10<H<13.5$ kOe the
local fundamental diamagnetic moment displays a very narrow diamagnetic step,
with a temperature width of the same size as the zero dc-magnetic field
transition. For higher field this step is transformed to a peak which is
related with the peak effect in the screening current. Finally, for $H<10$ kOe
the diamagnetic step is transformed to a gradual transition. Our findings for
the vortex matter phase diagram for the MgB$_2$ are closely related with
theoretical predictions concerning the vortex matter phase diagram of a type II
superconductor in the presence of weak point disorder.
