Willey has been called up for the three-match T20 series that starts in Cardiff on Wednesday and also for the three-match one-day international series that directly follows it.
If chosen for the subsequent one-day international series and T20 series of the same length against Pakistan, Willey would miss the rest of the T20 Blast group stage and also the County Championship matches away to his former club, Northamptonshire, and the eagerly-awaited tussle with Lancashire at Scarborough.
Willey has not played ODI cricket since last August or T20 international cricket since May, 2019.
Martyn Moxon, the Yorkshire director of cricket, said: “We’re pleased for Dave personally – obviously anyone who gets called up to play for England you’ve got to be pleased for them – but for us it’s clearly a big loss, our captain for T20, and also when we’ve got him back playing well for us in Championship cricket.
“So, from a Yorkshire point of view, it’s a big miss, a big blow, but it’s great for Dave and we wish him well.
“I just hope that he plays and that he’s not sat watching on the sidelines.
“They kind of binned him off just before the (2019) World Cup, and it’s not been mentioned for two years almost, so I just hope he plays and gets his chance.”
Willey, 31, was chosen for the T20 series as a like-for-like replacement for fellow left-armer Reece Topley, who suffered a side strain while playing for the Surrey second XI in a warm-up match for the T20 Blast.
England have now added another left-arm option in the form of George Garton to their ODI squad against Sri Lanka, with Warwickshire pace bowler Olly Stone the latest to go down after it was announced on Saturday that he will miss the rest of the season with a stress fracture of the lower back.
Jofra Archer (elbow) and Saqib Mahmood (abdominal) are also missing, while Ben Stokes (finger) is not expected to return to international action for another month.