If I understood your question correctly, the answer is yes. This is because, as the energy gap increases, the energy required for excitation increases. Since energy is inversely related to wavelength (E=hc/lambda), a shorter wavelength (higher energy)  light will be required for photo-excitation from its ground to the excited state. Thus we can say that the absorption wavelength for the material  has blue shifted or shifted towards lower wavelength or higher energy.

Dear Mallika,

Yes, it is called a blue-shift. Because as the band gap increases, the absorption shifts towards lower wavelength region, i.e., blue-region. The opposite to this is called the red-shift.

Good luck!