Tetanus prophylaxis should be administered immediately after injury to ensure prompt neutralization of tetanus spores, which can germinate quickly in devitalized tissues. Early administration maximizes the effectiveness of the tetanus toxoid and/or immunoglobulin in preventing toxin production. Delaying prophylaxis reduces its protective benefit and increases the risk of tetanus development. At the time of wound closure or after 24 hours is often too late, especially in contaminated wounds. Prophylaxis should not be withheld until infection develops, as tetanus is a toxin-mediated disease and infection may not be clinically apparent immediately.

Reference: Tintinalli's Emergency Medicine: A Comprehensive Study Guide, 9th Edition.