In a major organisational reshuffle, Shah promoted some young secretaries giving them charge of states and sought to strike a balance between experience and youth.
Mathur had contributed to the party's efforts in the Maharashtra assembly polls where the Bharatiya Janata Party (BJP) emerged as the single largest party for the first time and is poised to form the government.
The reshuffle indicated the steady rise of Nadda, a party general secretary, in the party ranks. Nadda is a member of the party's parliamentary board.
Party general secretary Rajiv Pratap Rudy, who had coordinated the party's poll effort in Maharashtra, has been given charge of Tamil Nadu and Andhra Pradesh.
Party MP from Punjab Avinash Rai Khanna will hold fort in poll-bound Jammu and Kashmir.
T.S. Rawat, a party leader from Uttarakhand, has been assigned poll-bound Jharkhand.
Winning the next assembly poll in Uttar Pradesh is crucial for the BJP in its efforts to improve its national presence and gradually move towards majority in the Rajya Sabha.
BJP vice-president Purushottam Rupala will look after party-ruled Goa.
Two other vice-presidents Vinay Sashrabudhe and Dinesh Sharma have been given charge of Madhya Pradesh and Gujarat respectively, with the party in power in both states.
Vice-president Prabhat Jha has been allotted Delhi where there is talk of early state elections.
General secretary Bhupender Yadav will be incharge of Bihar, where the BJP will face a major challenge in next year's assembly polls.
Other secretaries given states or union territories include Anil Jain (Haryana), Shrikant Sharma (Himachal Pradesh), Arun Singh (Odisha), Ramen Deka (Arunachal Pradesh), Poonam Mahajan (Dadra and Nagar Haveli, Daman and Diu), H. Raja (Kerala and Lakshadweep), Shyam Jaju (Uttarakhand) and Sidharth Nath Singh (West Bengal).
Party general secretary Ram Shankar Katheriya has been chosen for Chhattisgarh and Punjab while P. Murlidhar Rao, also a general secretary, will oversee Karnataka.
The party appointed Mahendra Singh as incharge of Assam, P.K. Krishnadas of Telangana and Sunil Deodhar of Tripura.