The 24-year-old, who has started the campaign in promising fashion for United, will stay at home, along with Anthony Martial, Donny van de Beek and Aaron Wan-Bissaka.
None of the quartet trained at Carrington on Wednesday morning ahead of the flight to Moldova.
Erik ten Hag is otherwise taking a full strength squad, with Cristiano Ronaldo among the travelling party and Luke Shaw returning after injury.
United are looking for their first points of their Group E campaign, having lost to Real Sociedad last week.
Rashford, Jadon Sancho and Harry Maguire, meanwhile, will be hoping for England call-ups this week as they ultimately target a place in Gareth Southgate’s World Cup squad.
The Three Lions face Italy and Germany in the Nations League later this month, the double-header the last chance Southgate has to look at players before their World Cup campaign begins against Iran in Doha on November 21.
Southgate has stuck by United captain Maguire in recent months despite his questionable form at the heart of the Red Devils’ defence – but he has now lost his place under Erik ten Hag.
Maguire started the opening two games of the season, including a 4-0 loss at Brentford, but has been warming the bench in the Premier League since then.
A lack of other genuine contenders could see Maguire keep his place, with Aston Villa’s Tyrone Mings also not enjoying the best start to the campaign.
Conor Coady joined Everton on loan from Wolves to bolster his own chances, with Marc Guehi and Fikayo Tomori also options, while Ben White has been playing at right-back for Arsenal.
There is also intrigue over United forwards Rashford and Sancho, the duo having been left out of the Nations League squad in June. Rashford has not played for England since missing his penalty in the shoot-out loss to Italy in the European Championship final at Wembley last summer, while Sancho – who saw his spot-kick saved – has featured just once.
Sancho has scored twice this season while Rashford has hit three goals in six Premier League games under Ten Hag.
As their respective form and confidence improves, they could force their way back into Southgate’s thinking, especially with Jack Grealish having started just one Premier League game for Manchester City this season and Jesse Lingard almost certainly missing out despite playing regularly at Nottingham Forest.
Another United player could be in limbo as Luke Shaw also lost his place in Ten Hag’s side after the losses to Brighton and Brentford.
With Shaw unfavoured with his club, Southgate could again utilise Newcastle’s Kieran Trippier at left-back but does have more natural options there in the shape of Ben Chilwell and Tyrick Mitchell or potentially a senior call-up for Ryan Sessegnon.
Southgate has always championed the idea of selecting players based on their form, meaning Brentford striker Ivan Toney has arguably never had a better chance of being included for the first time.
Captain Harry Kane will no doubt be involved as he continues to bear down on the England goalscoring record but Toney is the most in-form back-up option to the Tottenham man, having scored five in six Premier League games.
Goalkeeper Jordan Pickford is sidelined with a thigh injury so, with Aaron Ramsdale and Nick Pope likely to be included, Dean Henderson could earn a recall as he impresses on loan at Nottingham Forest.
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