Chahar impressed for India A in the tri-series against West Indies A and England Lions and was also effective for this year's Indian Premier League (IPL) champions Chennai Super Kings, with the 25-year-old collecting 10 wickets in 12 matches.
Bumrah is expected to be fit for the three-match one-day international series against England starting on July 12.
The BCCI said that Sundar, who last played for India in their T20 win over Bangladesh in March, sustained a right ankle injury in training before the first Ireland match and is expected to miss both the upcoming limited-overs series.
All-rounder Krunal Pandya has been named as Sundar's replacement in the T20 squad, while Axar Patel will take the 18-year-old's place in the ODI team.
(Reporting by Aditi Prakash in Bengaluru; Editing by Hugh Lawson)
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