The 30-year-old left-back went under the knife in May and missed the final two games of the Premier League season as well as England’s European qualifier in Slovenia.
Toffees boss Roberto Martinez revealed at the end of last season that Baines had been struggling with the problem for the past three years but said the surgery was “straightforward”.
Fellow left-back Bryan Oviedo will also miss the trip as he recovers from a broken toe meaning England Under-21 international Luke Garbutt, who recently signed a five-year extension, will have a chance to shine in Asia.
Republic of Ireland international midfielder Darron Gibson will also remain behind at Finch Farm as he attempts to return from a broken foot.
Martinez told the club’s website: “All three players are coming on really strong in relation to their respective rehabilitation programmes.
“Although they won’t be taking part in the tour they could be back playing a part with the team even sooner than anticipated.
“Leighton is well ahead of where we expected him to be at this point and all three will be there or thereabouts for the start of the season.”
New signings Tom Cleverley and Gerard Deulofeu have been included in a 24-man squad.
Everton kick-off their pre-season fixtures at League One club Swindon on Saturday before travelling to the Far East. Martinez’s side will face Stoke on July 15 before a second game against either Arsenal or a Singapore Select XI three days later.
Meanwhile, young Warrington-born defender Matthew Pennington has signed a new three-year deal to remain at the club until the summer of 2018.