The defence ministry said the missile was launched from a MiG-31 jet that took off from an airfield in southwest Russian Federation on Saturday.
The weapon, created to eliminate targets on the ground and at sea, hit its assigned target at a training ground, the ministry said, and described the launch as "normal".
Set to rousing, patriotic music, the video then shows a missile detaching from the airborne plane and gliding across the dark sky, leaving a fiery trail behind.
On 1 March, Mr Putin described the Kinzhal missile - named for a type of dagger - as "an ideal weapon".
The MiG-31 departed from an airfield in the Southern Military District within the framework of a testing air alert. The video appears to show a military jet carrying a missile.
"Secondly, we don't have this quantity of tools", he said.His remarks about Russian Federation not having the ability to affect or interfere with USA elections came just a few days after he announced that his country had developed a new type of nuclear weapon. Tests of this nature also help the ground crews and all other military personnel involved to get familiar with the new missiles.
Pentagon spokeswoman Dana White downplayed Putin's comments, saying the US military was capable of defending the country from any threats. "The attempt at curbing Russian Federation has failed", Putin said.
The Russian leader's comments come in a new two-hour documentary released online ahead of the upcoming presidential election in which he is the strong favourite.
Putin's recent refusal to extradite them, the Democrats said, was "simply unacceptable" and the USA should challenge that through diplomatic channels or an global arrest warrant.
"I told them: act according to the plan", Putin said, adding that shortly afterwards he arrived at the Olympic venue with the International Olympic Committee officials. "They did not impact any need on our side for a change in our deterrent posture".
"At the end of the day, they can sink all that money in; it does not change my strategic calculation", he said.