Iyer has led from the front and has been the team's leading run-getter in the tournament with 266 runs at an average of 33.25. There was no official update given on the extent of his injury.
Also seen in the nets was Rishabh Pant, who was not picked in India's World Cup squad announced on Monday.
Young opener Prithvi Shaw, who has not made an impact in his last five innings, was engrossed in a lengthy chat with team advisor Sourav Ganguly on the sidelines of the training session.
Delhi Capitals are on course for their first play-off appearance since 2012, having won five out of their eight games. They are second on the points table with 10 points.