Radar Online obtained an audio recording in which Gibson supposedly admits to punching the Russian singer, saying that she "deserved it".
According to TMZ, the website's claims prompted officials at the LA County Sheriff's Department to open a domestic violence investigation.
A spokesperson for the Sherriff's Department said in a statement that investigators are "currently gathering information regarding the allegations".
The Braveheart star denies the accusations and the audio file has yet to be made public.
Gibson and Grigorieva split up earlier this year but the pair are now involved in a legal battle over visitation rights to their baby daughter Lucia.
