Context. Large numbers of deep optical images will be available in the near future, allowing statistically significant studies of low surface brightness structures such as intracluster light (ICL) in galaxy clusters. The detection of these structures requires efficient algorithms dedicated to this task, which traditional methods find difficult to solve. Aims. We present our new detection algorithm with wavelets for intracluster light studies (DAWIS), which we developed and optimized for the detection of low surface brightness sources in images, in particular (but not limited to) ICL. Methods. DAWIS follows a multiresolution vision based on wavelet representation to detect sources. It is embedded in an iterative procedure called synthesis-by-analysis approach to restore the unmasked light distribution of these sources with very good quality. The algorithm is built so that sources can be classified based on criteria depending on the analysis goal. We present the case of ICL detection and the measurement of ICL fractions. We test the efficiency of DAWIS on 270 mock images of galaxy clusters with various ICL profiles and compare its efficiency to more traditional ICL detection methods such as the surface brightness threshold method. We also run DAWIS on a real galaxy cluster image, and compare the output to results obtained with previous multiscale analysis algorithms. Results. We find in simulations that DAWIS is on average able to separate galaxy light from ICL more efficiently, and to detect a greater quantity of ICL flux because of the way sky background noise is treated. We also show that the ICL fraction, a metric used on a regular basis to characterize ICL, is subject to several measurement biases on galaxies and ICL fluxes. In the real galaxy cluster image, DAWIS detects a faint and extended source with an absolute magnitude two orders brighter than previous multiscale methods.