Malawania anachronus was named by Fischer et al. (2013). Its type specimen is NHMUK PV R6682, a partial skeleton (Articulated partial skeleton comprising a fragmentary skull, cervical and thoracic vertebrae, ribs, partial shoulder girdle and a nearly complete left forefin), and it is a compression fossil. Its type locality is Chia Gara, which is in a Hauterivian/Barremian marine horizon in Iraq. It is the type species of Malawania.