The sketch featured a likeness of world number two Nadal being pulled over by police for speeding after he filled the gas tank of his car from his own bladder.
At the end of the sketch appeared the message: "Spanish athletes. They do not win by chance," along with the logos of the tennis federation and several other Spanish sports bodies.
The advert was broadcast on Monday after the Court of Arbitration for Sport banned Spanish cyclist Alberto Contador for two years following a positive test for the banned substance clenbuterol during the 2010 Tour de France.
"The Spanish federation will sue Canal+ for broadcasting a video which, aside from making unacceptable and slanderous insinuations, used the logo of the federation," the body said in a statement.
The federation said it would demand that the station not broadcast the sketch again, refrain from using its logo in the future and would ask for an undisclosed amount of money in compensation.
It will also contact the other Spanish sports federations whose logo featured in the sketch to see if they would like to take joint legal action against Canal+.
"On this occasion intolerable limits have been crossed and the tennis federation cannot ignore such discredit and slander towards our athletes," the president of the federation, Jose Luis Escanuela, said in the statement.