According to Ajit Agarkar, Shreyas Iyer is fit at the moment

Since suffering a back ailment in March, Iyer has missed a lot of cricket. He picked up an ache when he rejoined the team for the Asia Cup, when he only managed one knock.The senior selection committee of the BCCI believes that Shreyas Iyer’s fitness difficulties are behind him and that all that remains is for him to earn enough game time and runs before the World Cup.