In this paper, we report on a biospeckle laser method used to monitor a specific drug action on T. cruzi parasites. Experimental results from fast biospeckle monitoring of the parasites' activity under the influence of the drug demonstrate the effectiveness of the proposed method. We measure the speckle parameters such as spatiotemporal correlation and speckle grain size to assess the immediate action of the drug on the parasites during a very short incubation period. From a practical point of view, this aproach allows us to validate biospeckle as a fast, non-invasive and alternative method to test candidate drugs on T. cruzi parasites.