In this article, an efficient wavelet collocation method is proposed for solving the fractional bioheat transfer model within the skin tissue under intense moving heat source. Unlike the existing operational methods based on orthogonal functions, we formulate the Haar wavelet operational matrices of fractional order integration without using the block pulse functions. The thermal damages in the skin tissues are investigated by the extent of the denatured protein employing with the Arrhenius equation. The temperature distribution over the skin tissue has been investigated for different values of the fractional parameter α and moving heat source velocity v. The numerical outcomes suggest that the desired temperature decrease with an decrease in the order of the fractional derivative and moving heat source velocity. The numerical outcomes of thermal injuries and temperatures distributions are introduced graphically.