She was sacked by Hungary's N1TV station, which is affiliated to the far-right Jobbik party.
The station said in a statement that she had shown "unacceptable behaviour".
Hungary has become a key transit point for migrants on the journey towards Western Europe, with more than 150,000 people arriving this year.
Hungary's leaders have been criticised for what has been perceived as a harsher stance than other European states towards migrants.
Prime Minister Viktor Orban has warned of Hungary being "overrun" with refugees who threatened to undermine Europe's "Christian roots".