  We calculate analytically the R\'enyi bipartite entanglement entropy
$S_{\alpha}$ of the ground state of $1+1$ dimensional conformal field theories
(CFT) after performing a projective measurement in a part of the system. We
show that the entanglement entropy in this setup is dependent on the central
charge and the operator content of the system. When the measurement region $A$
separates the two parts $B$ and $\bar{B}$, the entanglement entropy between $B$
and $\bar{B}$ decreases like a power-law with respect to the characteristic
distance between the two regions with an exponent which is dependent on the
rank $\alpha$ of the R\'enyi entanglement entropy and the smallest scaling
dimension present in the system. We check our findings by making numerical
calculations on the Klein-Gordon field theory (coupled harmonic oscillators)
after fixing the position (partial measurement) of some of the oscillators. We
also comment on the post-measurement entanglement entropy in the massive
quantum field theories.
