Markram injured his finger while fielding and will be undergoing surgery
Boult will fly to New Zealand after the second Test.
Markram lashed out at a solid object during the Pune Test.
After a couple of minutes, Aiden Markram came to help his teammate as he knew where the ball was and picked it up.
India have confirmed their playing XI.
Apart from Markram and Bavuma, none of the batsmen could spend their time in the middle.
The visitors will need their youngsters to get acclimatized to the Indian conditions.
The tour starts from August 29 with the One-Day series.
Rassie van der Dussen has a batting average of 88.25 in ODI cricket.
Fidel Edwards added to the Hampshire squad in the place of Brad Wheal.