The Prime Minister of India, at the time of his/her appointment:

According to the Constitution of India, the Prime Minister is appointed by the President [2]. While the Prime Minister is typically a member of either the Lok Sabha or the Rajya Sabha, a person who is not a member of either House of Parliament can also be appointed to the position [3]. However, Article 75(5) stipulates that a minister (including the Prime Minister) who is not a member of Parliament for any period of six consecutive months shall, at the expiration of that period, cease to be a minister [1]. This means the appointee must secure a seat in either the Lok Sabha or the Rajya Sabha within six months of their appointment [3]. Historical precedents include Prime Ministers like Indira Gandhi and Manmohan Singh, who served while being members of the Rajya Sabha rather than the Lok Sabha [1].

Sources

1. [2] Laxmikanth, M. Indian Polity. 7th ed., McGraw Hill. > Chapter 21: Central Council of Ministers > Article 75-O ther Provisions as to Ministers > p. 213
2. [3] Laxmikanth, M. Indian Polity. 7th ed., McGraw Hill. > Chapter 21: Central Council of Ministers > APPOINTMENT OF MINISTERS > p. 214
3. [1] Indian Polity, M. Laxmikanth(7th ed.) > Chapter 13: Parliamentary System > 136,(/ Indian Polity > p. 136