"We will be without Vaasy for the final Test," SLC spokesman Samantha Algama told AFP. "He is going to back to England."
Vaas, 33, who had joined Middlesex at the start of the English season, returned home to play against Bangladesh and scored a maiden Test century in the first Test.
But with Sri Lanka having taken a decisive 2-0 lead in the three-match series, Vaas was given permission to honour the rest of his contract with Middlesex.
Sri Lanka won both matches by innings margins and look set for a clean sweep when the final Test starts at the Asgiriya stadium in Kandy on Wednesday.
All-rounder Farveez Maharoof, left-arm spinner Sujeewa de Silva and leg-spinner Malinga Bandara are standing by to replace Vaas, who has claimed 319 wickets in 98 Tests.
Barring injuries, Vaas will play his 100th Test against world champions Australia in Hobart in November.
Off-spinner Muttiah Muralitharan, who is contracted with Lancashire, will also return to England after the Kandy Test. Both Vaas and he will miss the upcoming three one-dayers against Bangladesh.
Meanwhile, Bangladesh have summoned middle-order batsman Tushar Imran from Dhaka to reinforce the team for the Kandy Test.
Imran, who has played four Tests and scored 55 runs, was a surprise omission from the Test squad even though he was selected for the one-day matches.