The all-rounder, who already has a two-year-old daughter with his wife Trish, told Reuters today that the birth could clash with the first Test starting in Colombo on July 27 because the tour dates had been brought forward.
''We had planned it for before the tour started, but now they've moved the tour earlier. The caesarean will take place on either July 21 or 25 and obviously I'll be trying to get to Sri Lanka straight afterwards.
''I might miss the first Test, but Cricket South Africa are happy because it really wasn't our fault with the tour dates changing,'' added Pollock, who flew home from the 2003 tour of England for the birth of his first child.
Haroon Lorgat, the convenor of the national selection panel, confirmed that he was not concerned about Pollock's possible absence.
''There's only a very small probability of him not making it in time for the first Test. We depart on July 19 and the birth is a day or two later, after which Shaun will leave,'' he told Reuters.
''But it's not an issue because we'll have back-up in the squad and I am keen to rotate and rest players,'' Lorgat told Reuters.
''All our planning suggests Shaun will only be a day or two late though.'' Top batsman Jacques Kallis has already withdrawn from the tour as he is recovering from elbow surgery, meaning South Africa could be without both their leading run-scorer and leading wicket-taker for the first Test.
South Africa and Sri Lanka will play two Tests, with a five-match triangular series with India completing the tour.