Bracewell admitted using cocaine but maintained that his use occurred out-of-competition, being prior to midnight on the day before the match, and that it was unrelated to sport performance.
Henry was ruled out of the white-ball series against Pakistan and India after suffering abdominal strain on the final day of the second Test in Karachi.
New Zealand won the one-off T20I after routing Sri Lanka in Tests and ODIs.
Doug Bracewell was rushing home after hearing of death of pet parrot, his lawyer said.
Mumbai ended the day at 431 for five in reply to New Zealand's 324 for seven declared on the opening day
New Zealand paceman Doug Bracewell suffered a shoulder injury during Kiwis' defeat by an innings and 52 runs against Australia in Wellington.
Adam Voges was bowled by Doug Bracewell without playing a shot. The umpire called no ball although television replays showed it was a legitimate delivery.
Adam Voges was bowled in the last over of the day by Doug Bracewell, only for umpire Richard Illingworth to signal a no ball. Television replays, however, confirmed it was a legitimate delivery.
At the close, Australia were 54 for two with skipper Steve Smith (24 not out) and Adam Voges (9) at the crease, trailing New Zealand by 148 runs.
Doug Bracewell was dropped from the Black Caps in February after embarking on a late-night drinking session with batsman Jesse Ryder on the eve of a Test against India.