The decision came after the demise of his mother earlier this week.
Herath, however, will join the team for the three-Test series, which will take place after the conclusion of the One-dayers.
He became the second senior player to opt out of the series due to personal reasons after former Sri Lanka captain Mahela Jayawardene made himself unavailable for both Twenty20 Internationals and ODI series.
Ajantha Mendis, who was to leave the team after today's second and final T20 game, will now stay on as a replacement of Herath, Sri Lanka Cricket announced.