Kumari, who is an MLA from Dalhousie in Himachal Pradesh, has served in various capacities in the party. She is a relatively a lesser known face compared to Nath who was a cabinet minister in the previous UPA government.
Her appointment is apparently aimed at avoiding any controversy ahead of the Assembly polls in Punjab next year.
Party sources had earlier said that in Punjab the leadership could make a temporary appointment of an existing general secretary till a decision is taken on induction of new leaders in the AICC secretariat.
He has refuted the allegations against him.
Nath has said that he was "hurt" by the developments wherein an "unnecessary controversy" has been created around the "tragic" 1984 riots.
The riots had followed the assassination of Indira Gandhi.