Anderson, 33, has not recovered from a right shoulder injury sustained in the third Test against Sri Lanka last month — a three-match series England won 2-0.
The Lancashire paceman’s place in the squad has been taken by uncapped Middlesex seamer Toby Roland-Jones.
He will now be pushing for a Test debut on his Lord’s home ground alongside Nottinghamshire quick Jake Ball, in the squad for the Sri Lanka series but also yet to make his maiden Test appearance.
“Jimmy has been touch and go for a while, he is making really good progress but it is the selectors’ view that he just won’t be quite ready for that first Test, hopefully for the second (at Old Trafford),” said England captain Alastair Cook on Thursday.
With struggling number three Nick Compton taking time out of cricket, the selectors have recalled Yorkshire’s Gary Ballance for the first of a four-Test series starting on July 14.
But they opted against including one-day wicket-keeper Jos Buttler in the Test squad and playing all-rounder Ben Stokes, not fit for bowling following a knee injury, as a specialist batsman.
Roland-Jones, 28, has been in fine form for Middlesex this season, with 30 County Championship wickets at under 30 apiece.
“Toby has had a really good summer so far and has been there or thereabouts for the last three years or so,” added Cook at a press conference.
“His bowling stats have improved a lot and he is a very decent bowler and it will be good to see him around the squad for the first time this week.”