The 25-year-old had looked set to play his first game since the row over his protracted move to Chelsea began, but it is understood that an existing injury to his ankle has flared up since he arrived in South Africa and he will therefore not take part in the game in Polokwane.
The star has missed parts of two training sessions but the injury is only minor and there are no plans to send him home.
Modric has been at the centre of a tug-of-war between his current employers and the Blues since they lodged a £22million bid for the player a month ago.
An improved offer of £27million and a transfer request from Modric are reported to have followed, but Spurs have remained steadfast in their determination to hold on to their star midfielder and insist he will begin the season as their player.
The Croatia playmaker is reported to have submitted his transfer request on the eve of the club's departure for their pre-season tour of South Africa, but he still travelled with the squad.
Modric has refused to talk to the media since he arrived in South Africa but there are no indications that the transfer saga means he will not give his all on the tour.
Dimitar Berbatov sulked his way through pre-season to speed up a move to Manchester United in 2008 but assistant manager Kevin Bond and captain Michael Dawson have both said Modric has not been affected by the furore surrounding his future while on tour.
Nevertheless, the injury has prevented Modric from playing in the first match of the tour, which is due to end next Sunday.
The next few days will be crucial in determining Modric's future.
Redknapp is due to fly out to South Africa to meet up with the squad on Sunday and will surely sit down with the player to discuss his future, mindful that having an unhappy player in the ranks could affect team morale ahead of what is a crucial season for the Londoners.
It is also possible that Chelsea could take their bid past the £30million marker ahead of their pre-season tour of the Far East, which begins on Thursday.
Back at Tottenham's base in Essex, midfielder Sandro is expected to undergo tests this evening to determine the extent of a knee injury he suffered on international duty on Monday.