World football's governing body is suffering the worst corruption scandal in its more than 100-year history and Blatter has been suspended from his post pending a full investigation. He denies any wrongdoing.
U.S. prosecutors have charged 41 entities and people including football bosses from across the Americas in a case they say involves $200 million in bribes and kickbacks tied to the marketing of major tournaments and matches.
"Not a single country has the right to spread its jurisdiction to other states, to say nothing of international organisations," Putin said during his annual news conference, in a clear swipe at the United States.
"This does not mean at all that one should not fight corruption ... But we believe this practise, when in various parts of the world they snatch foreign citizens and drag them out to be interrogated and prosecuted, is unacceptable."
Blatter is also the subject of a criminal investigation in his native Switzerland. In a letter published on Wednesday he again proclaimed his innocence in the corruption scandal. He is due to testify this week to FIFA's ethics panel.
"Whether there are signs of corruption in FIFA, the investigation must show. As for Joseph Blatter, he is a very respected person, he has done a lot for the development of world football," Putin said.
"He has always tried to treat football not as a sport but as an element of cooperation between countries and peoples. He is the one who must be awarded the Nobel Peace Prize."
Putin also targeted critics who allege that corruption may have been behind FIFA's decision to award Russia the right to host the World Cup in 2018.
"We know firmly one thing - that we received the right to host the World Cup in an absolutely honest and competitive fight," the Russian leader said.
(Reporting by Maria Tsvetkova, Alexander Winning, and Christian Lowe; Writing by Maria Kiselyova and Dmitry Solovyov; Editing by Gareth Jones)
