Two videos of the incident show a man standing by some cars and military vehicles in a wooded area and looking up at two KA-52 "Alligator" helicopters as they approach.
The press service did not say when the incident occurred and it was not clear whether it was denying that it happened during Zapad 2017, which started on September 14.
The online 66.ru portal said the accident happened on either Sunday or Monday at the Luzhsky range, 60 miles east of the Estonian border, during the Zapad-2017 drills, which have alarmed some of Russia's close neighbours.
The Russian military acknowledged that a rocket was sacked by accident by a helicopter, but insisted that no one was hurt in the incident.
Independent news site Fontanka.ru said one of the people was left with concussion but did not give details on the source of the video. Russian Federation launched short range ballistic missiles, naval forces, and its newest Ka-52 attack helicopters. The 66.ru report quoted a military source who said three people were injured, but a Russian military spokesperson said there were no injuries.
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The Zapad joint strategic exercise, with troops from Russian Federation and the Republic of Belarus, started on September 14.
A ministry spokesperson told the Russian news agency Interfax that the helicopter's targeting system had accidentally locked onto one of the parked vehicles while the aircraft were taking part in a different army exercise: practicing hitting ground targets.
As commander-in-chief of Russia's armed forces, Mr Putin observed the simulated battles along with a number of top generals at the start of this week.
The major exercises have elicited criticism from North Atlantic Treaty Organisation and the USA, who say Russian Federation has concealed the true number of troops taking part, and troubled some observers in Eastern Europe, where the Kremlin's invasion of Crimea in 2014 remains fresh.