A key component of the side that won the 50-over World Cup in 2019, Woakes has not featured in the shortest format at international level since November 2015.
Willey, meanwhile, will hope to get the chance to impress ahead of the T20 World Cup, which is scheduled to take place in October and November this year.
Liam Dawson is also included in a 16-man party that is minus the services of injured trio Jofra Archer, Ben Stokes and Reece Topley.
“With the T20 World Cup only a few months away, this summer is about perfecting our team and continue to progress on the field,” England head coach Chris Silverwood said.
“We want to approach every series with an influx of players aiming to win every match and giving us the best preparation as we get closer to the tournament.
“With several high-profile players missing through injury, it allows me to look at some of our experienced players who have not featured at this level for some time.
“The likes of Chris Woakes and David Willey are very experienced cricketers, and to have them both in the mix is exciting and shows the depth of squad we have available.
“I want our team to play an attacking form of the game. I hope we can continue to excite the England fans with our approach.”
The three-match series begins in Cardiff on June 23, with the second game also taking place at the same venue the following day. The Ageas Bowl will then host the finale on June 26.
England squad for T20 series against Sri Lanka:
Eoin Morgan (captain), Moeen Ali, Jonathan Bairstow, Sam Billings, Jos Buttler, Sam Curran, Tom Curran, Liam Dawson, Chris Jordan, Liam Livingstone, Dawid Malan, Adil Rashid, Jason Roy, David Willey, Chris Woakes, Mark Wood.
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