He said he wished Trump a speedy recovery, praising the 74-year-old's "innate stamina".
In a telegram, Putin said: "I am sure that your innate stamina, high spirits, and optimism will help you cope with this deadly virus."
It comes hours after Trump and Melania were revealed to have coronavirus and were entering quarantine "immediately".
Taking to his favourite mode of communication, Twitter, the US president said: "Tonight, @FLOTUS and I tested positive for Covid-19.
"We will begin our quarantine and recovery process immediately. We will get through this TOGETHER!"
Earlier, it was confirmed top White House aide Hope Hicks had tested positive for coronavirus.
Other world leaders have also sent their best wishes to the president, including Prime Minister Boris Johnson.
The PM tweeted earlier: "My best wishes to President Trump and the First Lady. Hope they both have a speedy recovery from coronavirus."
Johnson had his own brush with the disease earlier this year and was briefly in intensive care battling the virus.
Trump is in a high-risk category for Covid-19 due to his age and because he is considered overweight.
On Thursday night, the president had confidently claimed that the end of the pandemic was in sight.
He has spent months downplaying the seriousness of Covid-19 and has been widely condemned for how he has handled the crisis, which has seen the US suffer the world's highest number of cases and deaths.
More than 212,000 people have died in the US, while almost 7.5 million people have tested positive, more than a fifth of the total number of cases worldwide.
In one particularly grim statistic, it was revealed that one in 1,000 people in the state of Mississippi, expected to vote heavily for Trump, have died from the virus.
His diagnosis, just over a month before the US election, has sparked chaos.
Trump and his Democratic opponent Joe Biden met for the first presidential debate, but news of the President testing positive has cast uncertainty over the next two debates.