Bravo sustained the injury during the tour of England and did not travel with the remainder of the squad to Ireland on Sunday.
He remained in London for specialist examination and treatment after which he will return to the Caribbean.
"We are going to miss Dwayne but we decided against replacement because it is a short trip with only three games and we've had some good performers in England who did not get a chance in the one-day internationals (ODIs) in England," West Indies coach David Moore said.
"Darren Sammy did well but unfortunately missed out in the ODIs and Austin (Richards Jr) and Lendl (Simmons) will also have a chance to stake their claims," the Australian added.
The West Indies play the Netherlands on July 10, Scotland on July 12 and Ireland on July 14 before returning home.
They lost a four match Test series against England 3-0 but came from 1-0 down to seal a 2-1 one-day series victory over their hosts with a 93-run win at Trent Bridge on Saturday.