Fellow spinner Ish Sodhi, who was originally only named in the T20 squad, will replace Astle in the ODI side.
Astle suffered the injury in a warm-up game between the Black Caps and a President Board's XI in Mumbai on Tuesday.
Further assessment and a scan confirmed Astle to have suffered a tear on his right side, which will see him ruled out for around three weeks.
Coach Mike Hesson said it was cruel timing for Astle.
"Todd was really impressive in the recent New Zealand A tour over here and had done everything he possibly could to get himself ready for this series," said Hesson.
"He deserved this opportunity and everyone in the team is certainly feeling for Todd. He'll return to New Zealand and get himself ready for a big summer," he added.
The ODI series begins on Sunday at the Wankhede Stadium in Mumbai.
ODI squad: Kane Williamson (capt), Trent Boult, Colin de Grandhomme, Martin Guptill, Matt Henry, Tom Latham, Henry Nicholls, Adam Milne, Colin Munro, Glenn Phillips, Mitchell Santner, Ish Sodhi, Tim Southee, Ross Taylor, George Worker. (ANI)