The left-armer hurt his left ankle during a fielding drill ahead of Monday's warm-up match against Pakistan at the Gabba.
He will be assessed in the build-up to Saturday's match in Perth, the 2010 champions said in a statement.
Jos Buttler's England are among the title favourites after back-to-back T20 series victories in Pakistan and Australia.
"We're definitely ready now," all-rounder Sam Curran (24) said.
"We're feeling like we're almost not peaking but we're playing good cricket.
"We're really excited, hopefully with a couple of good training sessions in Perth, come the weekend we'll be good."
England will be wary of any complacency against Afghanistan, especially as the tournament has already seen major upsets with former champions Sri Lanka and twice winners West Indies suffering shock defeats.
"It's T20 format, anything could happen," Curran said.
"Afghanistan are a side that are extremely skilful ... We know it's going to be a really tough opening game."
Curran's all-round ability was on display in Monday's warm-up match against Pakistan where he shared the new ball with Ben Stokes and smashed an unbeaten 33 off 14 balls to guide his team to a comprehensive victory.
"It's very challenging but it's just a role you've got to enjoy," he said.
"Guys like Moeen (Ali), (Liam) Livingstone, Harry Brook are experienced in that middle-over phase so they help me through it.
"There will be some days where it doesn't work, some days where it does."