Ben Stokes and Jos Buttler also left out
Anderson's absence has given uncapped Middlesex seamer Toby Roland-Jones an opening in England's 12-man squad, announced on Thursday. He will compete with Nottinghamshire's Jake Ball.
England and Pakistan will play four Tests, five ODIs and a one-off T20 international.
Yorkshire's Ballance, 26, was included in place of Nick Compton, who is taking a break from the game.
Ballance is back in the Test squad for the first time since the winter series in South Africa and could make his first Test appearance for England in 12 months.
"He has been in recent form with the bat for Yorkshire in the Championship. Gary is mentally strong and we feel that he will add quality and experience to England’s middle-order," said national selector James Whitaker.
Ben Stokes and Jos Buttler have been left out of the squad along with Lancashire bowler Anderson, who has not recovered after injuring his shoulder against Sri Lanka last month.
"With an injury to James Anderson, there is an opportunity for Toby Roland-Jones who has been a consistent performer in the County Championship over the last few years and deserves his chance," said Whitaker.
"Building on the success of the Test series win against Sri Lanka last month, we have maintained our objective of retaining a balanced squad," he added.
England won the Sri Lanka Test series 2-0.
The Lord's Test against Pakistan begins next Thursday.
England's squad for the first Test:
Alastair Cook (Essex, captain), Moeen Ali (Worcestershire), Jonny Bairstow (Yorkshire), Gary Ballance (Yorkshire), Jake Ball (Nottinghamshire), Stuart Broad (Nottinghamshire), Steven Finn (Middlesex), Alex Hales (Nottinghamshire), Joe Root (Yorkshire), Toby Roland-Jones (Middlesex), James Vince (Hampshire), Chris Woakes (Warwickshire).
IMAGE: Gary Ballance
Photograph: Andrew Couldridge/ Livepic/Reuters