The watchdog said the "criminal attack" by a Russia-based cyber-espionage group had released a second tranche of documents, including details of American and German athletes.
Wada first fell victim to the hackers on Tuesday when medical records relating to ''therapeutic use exemptions'' granted to certain athletes were made public.
The body confirmed on Thursday that another leak of "confidential athlete data" had taken place - although it did not identify the athletes affected.
The statement read: "Fancy Bear [aka Tsar Team (APT28)] have leaked another batch of confidential athlete data from Wada's Anti-Doping Administration and Management System (ADAMS).
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"Similar to the leak that the Agency announced on 13 September, this time the group released the confidential athlete data of 25 athletes, from eight countries, into the public domain.
"The targeted athletes include 10 from the United States, five from Germany, five from Great Britain, one from the Czech Republic, one from Denmark, one from Poland, one from Romania, and one from Russia."
The organisation revealed that hackers had illegally gained access to its anti-doping administration and management system database via an International Olympic Committee-created account for the Rio Games.
Wada director general Olivier Niggli said: "Wada is very mindful that this criminal attack, which to date has recklessly exposed personal data of 29 athletes, will be very distressing for the athletes targeted and cause apprehension for all athletes that were involved in the Rio 2016 Olympic Games.
There is no suggestion that any of the athletes have done anything wrong.