The experienced Dinesh Karthik, who led the state to a memorable triumph in the Syed Mushtaq Ali Trophy T20 tournament, has been named captain of the 20-member squad.
Left-arm pacer Natarajan, who became the first Indian cricketer to make his international debut across all three formats during the same tour in Australia, is not part of the India squad for the first two Tests against England in Chennai.
He was part of the XI that claimed the series-clinching win in the Brisbane Test against Australia after having his ODI and T20 debut during the tour.
All-rounder Baba Aparajith was named vice-captain of the team, according to a TNCA media release.
Tamil Nadu chief selector S Vasudevan said Natarajan has been picked in the squad but they are awaiting BCCI''s nod for him to play the tournament.
"Yes, we have selected Natarajan but the BCCI has to give the go-ahead for him to play in the tournament as they want to keep him fresh for the ODIs and T20s against England," he told PTI.
Also making a comeback to the team is medium-pacer K Vignesh, who missed the Mushtaq Ali Trophy after being diagnosed with COVID-19.
Vasudevan said it was a balanced squad with a mix of experience and youth, adding he expected it do well in the tournament.
He praised the Dinesh Karthik-led squad for wining the Mushtaq Ali Trophy in Ahmedabad on Sunday.
Tamil Nadu will be without the services of all-rounder Vijay Shankar, Sandeep Warrier and Jagannath Sinivas, who were in the SMAT squad.
Shankar sustained an injury in the first game and missed the rest of the team''s victorious campaign, while Warrier joined the India team in Chennai as a net bowler for the first two Tests.
Vasudevan said it was good to have Vignesh back in the team as he had done well last season but added they could not consider Shankar for selection as he has not recovered fully.
"It is good that Vignesh is back. He did very well last season. Vijay Shankar has not recovered fully and hence has not been included," he said.
The BCCI is yet to announce the dates for the Vijay Hazare Trophy.
Squad: K Dinesh Karthik (Captain), B Aparajith (Vice Captain), B Indrajith, K B Arun Karthick, C Hari Nishaanth, M Shahrukh Khan, N Jagadeesan, L Suryapprakash, M Kaushik Gandhi, J Kousik, M Ashwin, R Sai Kishore, M Siddharth, R Sonu Yadav, K Vignesh, T Natarajan, A Aswin Crist, Pradosh Ranjan Paul, G Periyasamy and M Mohammed.