Ex-French Minister for Health and Sport Roselyne Bachelot said Nadal's seven-month absence in 2012 was "probably due to a positive doping test".
Nadal, 29, has denied ever doping and the Spanish Olympic Committee said he had passed "countless doping tests".
Real Madrid have defended Nadal from "the attacks made on his person".
A club statement said: "Rafa Nadal represents the fundamental values of sport.
"His greatness and his incredible achievements have always been based upon a foundation of exemplary conduct, unwavering work, talent and astonishing levels of commitment.
"This being the case, our institution considers the attacks made on his person by former minister Roselyne Bachelot to be unjustifiable and unacceptable."
Real Madrid coach Zinedine Zidane added: "I feel bad for Rafa Nadal because he is a gentleman, a person that has shown the values he has and that everyone loves.
"He is a professional and I know him a little. I feel bad for what they have said.
"He has to leave all this to one side and think that everyone who loves sport, loves Rafa Nadal, whether they be French, Spanish or American."
Nadal, who has won 14 Grand Slam titles, was out for seven months from July 2012 with tendinitis and then a stomach virus.
The Spaniard was asked on Wednesday about the subject of doping, in the light of Maria Sharapova's admission last week of a failed test.
"I am a completely clean guy," said the former world number one. "I have never had the temptation of doing something wrong."

FAW officials have yet to decide how to commemorate the occasion after Fifa could not guarantee that there would not be disciplinary proceedings if a poppy was displayed.
England and Scotland will defy Fifa's ban on players wearing poppies in their meeting on Friday.
With the FAW yet decide their policy, Ledley said: ''We will support whatever decision they make.''
Fifa's regulations say players' equipment should not carry any commercial, personal, political or religious messages.
When the issue arose in 2011, a compromise was reached in which Wales players were allowed to wear armbands with the poppy symbol in a friendly against Norway.
Northern Ireland will mark Armistice Day by wearing plain black armbands in the World Cup qualifier against Azerbaijan in Belfast.
The Irish FA had requested permission from Fifa to wear a poppy on the shirt or armband.
Breaching Fifa regulations could result in a fine or even a loss of points and the FAW are set to leave a decision until as late as possible.
They have already planned a two minute silence during training on Armistice Day's on Friday and there will also be a tribute at the game regardless of whether poppies are worn.
Crystal Palace's Ledley said Wales' players are content to leave the decision over poppies to the Football Association of Wales.
''It is obviously out of our hands. It is dealt with by the FA of Wales," Ledley added.
"It is down to them too take the decision. We will support whatever decision they make.
''As players our job is just to concentrate on the game, I am sure the FAW will make the right decision.''
Real Madrid backed "exemplary" club member Rafael Nadal after the tennis star was accused by a former French minister of failing a drugs test.
[NEXT_CONCEPT]
Midfielder Joe Ledley believes the Football Association of Wales will make the ''right decision'' on how best to mark Armistice Day in the World Cup qualifier against Serbia.