The hosts were mauled by an innings and 92 runs in the first match which ended on the fourth day at the Sir Viv Richards stadium in Antigua.
Besides the 19-year-old fast bowler from Antigua, the selectors have retained the same squad which now contains 14 players.
Joseph has only played 12 matches at the senior level, including eight first-class matches in which he has taken 24 wickets at an average of 24.45 with two five-wicket hauls. He was, however, one of West Indies' most impressive performers on their way to winning the Under-19 World Cup in February.
Joseph's addition will bolster the depleted attack which contained only one genuine quickie in Shannon Gabriel, supported by two medium pace bowlers and allrounders in Jason Holder and Carlos Brathwaite and leg-spinner Devendra Bishoo.
With India already 1-0 up in the four-match Test series, the hosts will aim to bounce back and draw level in the second match to be played at the Sabina Park from Saturday.