But athletes who can prove they are clean and have not previously been sanctioned will be allowed to compete.
Mr Putin rejected the claims and said the ban was "politically motivated".
There will be no Russian flags, anthems or uniforms during the Games in Pyeongchang. Russian athletes competing will carry a neutral flag and the name "Olympic Athlete from Russia", the IOC says.
Russian state TV channels have said the allegations are an anti-Russia witch hunt and have pushed the #NoRussiaNoGames hashtag.
But in his first comments after the IOC decision, Mr Putin said: "We will not be announcing any kind of blockade. We will not prevent our Olympic athletes from taking part if anyone wants to take part in a personal capacity."
He later added: "This all looks like an absolutely staged and politically motivated decision."
Earlier, Kremlin spokesman Dmitry Peskov said the situation was "serious" and required "deep analysis" but he called for Russians to avoid an "emotional" response.
Mr Peskov said it would be wrong to jump to conclusions until Russia's athletes had met and the IOC had been contacted.
He added that it would not be a priority to hold Russian officials responsible.
A member of the Russian parliament, Valery Rashkin, has filed a lawsuit against former Sports Minister Vitaly Mutko over the row. Mr Mutko has been accused of presiding over a systematic cover-up of doping in Russian sport.
Meanwhile, 22 Russian athletes have appealed to the Court of Arbitration for Sport over the IOC ban.
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