In present paper the effect of noise and error occurring due to noise in fractal dimension of digital images has been analyzed. For this purpose, three digital images have been used which are added by Gaussian noise, salt and pepper noise and speckle noise. The fractal dimension of both noisy and non-noisy images has been estimated and corresponding error is reported in terms of RMSE. The study shows that noise affects the fractal dimension and there is an increase in fractal dimension due to noise. The average percentage error in fractal dimension has been estimated and reported as an offset for finding actual fractal dimension from noisy images.