The sentences were handed out by the ethics committee of football's world governing body, Fifa on Thursday morning.
Blatter, secretary general Jerôme Valcke and Uefa president Platini are being investigated by the committee over corruption allegations. The three are now banned from any football activity for the next 90 days.
Former French international Platini is accused of accepting a €1.8 million "disloyal payment" from Blatter back in 2011.
"The grounds for these decisions are the investigations that are being carried out by the investigatory chamber of the ethics committee," Fifa said in a statement.
“The duration of the bans may be extended for an additional period not exceeding 45 days," Fifa added.
Platini denies all wrongdoing and recently told AFP that he had nothing to hide.
"I have known for a long time that I would be the target of many unfounded attacks and I am conscious that these attacks will continue until the Fifa elections take place. There is no doubt about my integrity," Platini said in an interview.
"I have done nothing wrong," he insisted.
The Frenchman, who is also Fifa's vice president, had hopes of succeeding Blatter in the top job and had formally submitted his application to become president on Thursday morning.
But the 90-day suspension could effectively end his chance of succeeding Blatter, who is the subject of a criminal investigation in Switzerland.
Although the ethics committee said the ban does not mean his candidacy is automatically void.
Platini, Blatter and Valcke all deny wrongdoing.