"This post-season fixture represented an opportunity for the club to visit supporters in South Africa for the first time in 19 years," the five-times European champions said on their website (www.liverpoolfc.com) on Friday.
"Regrettably the South Africa Premier Soccer League has decided this match cannot now be played on this date and have subsequently advised Ajax Cape Town this fixture should be cancelled.
"We are hugely disappointed we are unable to visit and the team cannot play in front of our terrific supporters."
South Africa's Premier League did not give permission for the fixture because it would have come four days before the country's FA Cup final.
"This is the biggest game of the season for our sponsor and we want them to get the exposure they deserve," said the league's general manager Derek Blankensee.