Shaw came off at half-time of United’s 2-0 Europa League quarter-final first-leg victory over Granada in Spain on Thursday night, though Solskjaer said his switch was to “protect” the England left-back.
Solskjaer also confirmed that Pogba had a “bit of a niggle” but is OK to play in north London.
Elsewhere for United, Anthony Martial, Phil Jones and Eric Bailly are all sidelined by injury.
The United boss has a couple of key calls to make with his starting XI: David de Gea started in goal on Thursday, but it would have been a surprise not to see Dean Henderson return against Spurs as the battle for No1 goalkeeper continues.
The defence is as you are with Shaw passed fit. In midfield, Scott McTominay is suspended for the return leg against Granada, and Fred comes in to add some bite.
Edinson Cavani is the go-to striker and gets the nod over Greenwood.
Manchester United XI: Henderson, Wan Bissaka, Lindelof, Maguire, Shaw, McTominay, Fred, Bruno Fernandes, Pogba, Rashford, Cavani
Subs: De Gea, Mata, Greenwood, Diallo, Alex Telles, Matic, Williams, Van de Beek, Tuanzebe
Injury list: Bailly, Jones, Martial