Murali is flying to Chennai in India because his child is unwell and is not expected to return for the remainder of the tour.
The off-spinner was once again the mainstay of Sri Lanka's attack during the Test series against England, taking 24 wickets at an average of 16.87 as the three-match encounter was drawn 1-1.
But he has been less of a factor during the ongoing One-day series, taking two wickets at an average of 49 apiece,
"He has already left (the team hotel) and is flying out tomorrow (Friday)," a team spokesman told the Press Association.
"His child is not well. At the moment we really don't know what the situation is. We hope to find out more tomorrow."
One reason why Murali, 34, has had less of a role in the One-dayers has been the performance of the rest of his team's attack.
Sri Lanka lead the five-match series 2-0, after a pair of convincing wins, with the third match at Durham's Riverside Ground on Saturday.
Only Australia leg-spinner Shane Warne has taken more than Murali's 635 Test wickets.
But no bowler in the history of Test cricket has more hauls of 10 or more wickets in a match than Murali's 16. His 53 returns of five or more wickets in a Test innings is also a record.
However, his career has been blighted by controversy over his unique action. He was twice no-balled for throwing during Sri Lanka's 1995/96 tour of Australia and again, also in Australia, in 1998/99.
Despite having his action cleared by biomechanical experts, Murali found himself in fresh trouble two years ago regarding his 'doosra' delivery, the ball that turns away from the right-hander rather than towards him as would a conventional off-spinner.
In March 2004 his 'doosra' was reported by International Cricket Council match referee Chris Broad, the former England opening batsman.
Further tests followed, which led to a relaxation of the rules regarding throwing at the elite level after an ICC investigation found many professional cricketers were in fact bending their arms in delivery, contrary to the Laws of Cricket.