The plane was travelling from Ukraine to Turkey when Putin was told it had been hijacked and was on its way to Sochi, where the opening ceremony was about to take place, according to the film.
Putin said he gave permission to shoot down the jet, which had 110 people on board, after security services told him that was the procedure in such situations.
The president was informed just before the ceremony that it was a false alarm -- the plane had not been hijacked and so was not brought down.
When interviewer Andrei Kondrashov asked how he felt during the time between the two calls, Putin said: "I'd rather not talk about that."
The two-hour documentary, released online on Sunday a week ahead of an election Putin is expected to win in a landslide, presents an overwhelmingly positive picture of the president.
The segment about the plane is intercut with images of fighter jets flying through the sky and shots of the Twin Towers on 9/11, with an action movie-style soundtrack.
"Everything's fine," an unshakeable Putin told International Olympic Committee head Thomas Bach after the incident, according to the film.
Putin's slogan in a lacklustre election campaign has been: "A strong president -- a strong Russia".
The documentary was produced and presented by Kondrashov, who is a spokesman for Putin's campaign.
It also features interviews with a number of the Russian leader's allies including former German chancellor Gerhard Schroeder.
Putin also said in the documentary that he would "never" give the Crimean peninsula back to Ukraine.
Running against a motley crew of seven challengers, Putin is expected to take nearly 70 percent of the March 18 vote with a turnout of more than 60 percent, according to state-run pollsters.
