Milne was one of Phoenix's star performers as the reached the final of the first edition of the competition, finishing joint-top of the wicket-takers' list, with 12, and the best economy (0.95 runs per ball) of any bowler.
The fast bowler last played at the IPL in March, and he was unable to feature in New Zealand's white-ball tour of Europe due to the same problem.
Dwarshuis, the Australia left-armer who won his first cap in Pakistan earlier this year, has previously played county cricket for Worcestershire.
He is due to arrive in the UK on Monday and will be available for the second half of the group stage, with Phoenix currently sitting on four points from three games.
"We're really pleased to be able to recruit such an experienced fast bowler in Ben," Craig Flindall, Birmingham Phoenix general manager, said. "Naturally, we're disappointed that Adam couldn't feature for us this year, but Ben will add a left-arm option to our exciting group."