The Hampshire man is the only member of the one-day squad who has not played a single match on the current tour of India, but was in contention to feature in the final fixture on Sunday, a dead rubber in Dharamsala.
But he was injured during a morning workout and has now been withdrawn from the Twenty20 squad for next month's trip to New Zealand, as well as the England Lions tour of Australia.
Briggs' disappointment has led to good news for Yorkshire's Joe Root, who has now been added to the T20 squad as a replacement.
Root, whose star is rising by the day, is now part of all three squads for the New Zealand tour.
He was named in the Test squad ahead of Eoin Morgan and Samit Patel on Thursday, as well as being a late addition to the ODI group.
An England and Wales Cricket Board spokesman confirmed: "Danny Briggs has been ruled out of the current one-day series, the New Zealand Twenty20s and the Lions tour with a right ankle sprain sustained during a fitness session.
"Joe Root will replace Briggs in the Twenty20 squad in New Zealand."
- Sports & Recreation
- New Zealand