The 35-year-old, Sri Lanka's most dangerous bowler, is recovering from a tendon strain in his right bicep, an injury that also ruled him out of the recent Twenty20 World Cup.
"I'll definitely miss the first three games in Dambulla and we'll assess the situation again towards the end of next week," Muralitharan told Reuters.
Sri Lanka captain Mahela Jayawardene hinted at his return being delayed until Sri Lanka's two-Test tour of Australia in November.
"We have a lot of Test cricket coming up so we need to make a sensible decision that protects him in the long-term," Jayawardene told the media.
England, though, are still preparing for Muralitharan and his supporting slow bowlers, leg spinner Kaushal Lokuarachchi and off spinner Dilruwan Perera, in conditions that are expected to favour spinners.
"We've been told he's going to be out for the first couple of games, but we're preparing as if Murali is playing and we will still prepare in this way," said England captain Paul Collingwood.
England have never won a one-day series on Sri Lankan soil.
