For Finn, it is the latest blow during an injury-hit period. He was ruled out of the tour of the UAE late December with a stress injury to his left foot and left the tour of South Africa early with a side strain he picked up during the third Test in Johannesburg.
"Really disappointed to have picked up another injury on my road to recovery," Finn tweeted.
"Gutted doesn't describe it. Good luck to the guys out there!"
In Finn's absence, Plunkett will form England's pace attack in the tournament alongside David Willey, Reece Topley, Chris Jordan and Ben Stokes.