Wilshere was in line for a first international appearance since Euro 2016, having battled back from persistent injury issues to regain a place in Arsene Wenger's first-team plans this season.
Speaking at a pre-match news conference, England boss Gareth Southgate played down fears the 26-year-old's latest setback was significant, and Wilshere could still feature when Italy travel to Wembley next week.
"Jack just felt some tendinopathy in his knee," Southgate said. "It's a problem he's had before, nothing too serious.
"We had the option to bring him here and treat him here but we've decided to have him back at base.
"There's a good chance he's with us on Saturday but we'll see how he responds.
"It's something that in the past has settled down very quickly so hopefully that will be the case. Lots of players have tendon issues that over time flare up.
"He's trained well with us this week and if you think about the journey he's been on over the last couple of years, the big injuries he's had to come back from. He's progressing really well."
We've arrived in the Netherlands, where Gareth Southgate has confirmed that @JackWilshere hasn't travelled – but the @Arsenal man remains in contention for Tuesday's game against Italy. pic.twitter.com/eDwwQ5pmWH — England (@England) March 22, 2018
Joe Hart only recently regained his first-team spot at West Ham after being dropped in December, while Stoke City's Jack Butland is also shy of his best form and in the midst of a relegation fight.
Uncapped Burnley keeper Nick Pope is in the squad for the first time – his opportunity in Sean Dyche's side have only come about due to still-sidelined England international Tom Heaton suffering a dislocated shoulder against Crystal Palace last September.
Pickford impressed in November's goalless draw with Germany and he will get a chance to shine once more when Ronald Koeman – the man who sanctioned a £30million move for the former Sunderland keeper while manager at Everton – takes charge of his country for the first time.
"He's a very agile keeper who is quick around his goal and capable of making big saves," Southgate said.
"His distribution is excellent which is a key part of how we want to play.
"It's a great opportunity for him. He played really well against Germany in November and it's another good opportunity for us to see him in another international game."