We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal polynomials. The Bialynicki-Birula-Mycielski inequality has also been tested for a number of states. (C) 2011 American Institute of Physics. [doi:10.1063/1.3566977]