The 2010 British Open champion was at 3-under 207 and tied for 32nd place after shooting even-par 70 in the third round.
Oosthuizen entered the Nelson with the No. 7 world ranking, the highest-ranked player in the field. He had missed the cut in his only other Nelson appearance.
Michael Bradley also withdrew on Sunday morning with a back problem. Bradley was 2 under.
Oosthuizen is also set to play in next week's Colonial. Bradley is not on the field list for that invitational tournament.
Since 72 players made the secondary cut after three rounds, Oosthuizen and Bradley will get paid equal to a 71st-place finish at the Nelson.