Brar, 26, will join the test squad in New Zealand and will not be available for Sunday's fifth and final one-day international in Tauranga.
India will not name a replacement for Brar, with the visitors leading the five-match ODI series 2-1.
Wicketkeeper-batter Rishabh Pant has linked up with the squad in Wellington after receiving fitness clearance.
The two-match test series begins on November 19th.
Test squad: Shubman Gill (captain), Yashasvi Jaiswal, KL Rahul, Devdutt Padikkal, Rishabh Pant, Dhruv Jurel, Ravindra Jadeja, Anshul Kamboj, Jasprit Bumrah, Prasidh Krishna, Akash Deep, Sai Sudharsan, Nitish Kumar Reddy, Washington Sundar, Mohammed Siraj, Gurnoor Brar
ODI squad for the fifth ODI: Shreyas Iyer (captain), Rohit Sharma, Virat Kohli, Tilak Varma, Ishan Kishan, Axar Patel, Naman Dhir, Auqib Nabi, Ruturaj Gaikwad, Arshdeep Singh, Kumar Kushagra, Mohammed Siraj, Yash Thakur, Kuldeep Yadav