Organisers played Die Stem van Suid-Afrika, widely associated with the apartheid-era, instead of the hybrid version of Nkosi Sikelel' iAfrika and Die Stem which has been used since 1997.
"We are extremely disappointed that an administrative blunder has been the source of much embarrassment for our team and all South Africans," said SA Hockey Association CEO Marissa Langeni.
"The anthem played caused our team much discomfort as they stood not knowing what to do with themselves.
"This incident has robbed our team of what should have been a moment of pride."
However, the mix-up didn't seem to trouble the South Africans too much as the world number 12 side went on to beat world number four Great Britain 3-1.
"Great Britain Hockey, the organiser of the Investec London Cup, offers a full and unreserved apology to the South African women's hockey team and their supporters for mistakenly playing the wrong national anthem before South Africa's match with Great Britain," said a British Hockey statement.
"The error was made by a contractor responsible for sports presentation at the event. Standard procedure would be to check anthems to be played with visiting teams in advance, however, on this occasion that did not happen and Great Britain Hockey accepts full responsibility.
"Great Britain Hockey and its contractor appreciate the sensitive nature of this unfortunate mistake and we apologise unreservedly for the offence caused.
"The correct anthem will be played before all of South Africa's remaining matches beginning with the team's second fixture against Germany on Wednesday evening.