The latest development in computing methodologies and related steganography based applications had created a novel practice such as telemedicine where patient diagnosis images or allied information can be used diagnosis practices that are located in remote areas. In order to provide accurate and effective telemedicine the flawless or seamless biomedical information is required from patient. With respect to this the medical data may remain prone to get corrupted by hackers or might get manipulated when transmitted through an insecure channel. The cryptosystems which are available are not efficient enough to solve the above mentioned issues. Hence, in this research work a much efficient and effective image steganography technique has been proposed in order to hide the confidential and important image information. We have incorporated Discrete Wavelet Transformation (DWT) technique instead of wavelet transform techniques to embed the secret message in the required cover images. Also, to assure continuous communication through insecure channel, a new model called ElGamal encryption cryptosystem model has been implemented which contains the steganography scheme which has been proposed and developed. To maintain the content of Region of Interest (ROI), Region of Non- Interest (RONI) is used to embed the secret information. The overall performance analysis reveals that the DWT with ElGamal encryption provides more efficient and also have high embedding capacity, imperceptibility when compared to other methods like Hamming code, Syndrome-Trellis Code (STC) and Rivest-Shamir- Adleman (RSA) based methods.