We present continuous wave photoinduced absorption spectroscopy of single-walled carbon nanotubes dispersed in a polymer matrix. The spectrum is dominated by a modulation of the absorption line shape, predominantly of large diameter tubes, that we assigned to electroabsorption caused by local electric fields arising from trapped photoinduced charges. The lack of selectivity in the excitation points to an efficient migration of the photoexcited states, either the singlet excitons or the charges resulting from their dissociation.