The government says a police officer flew the helicopter over the capital, Caracas, and dropped grenades.
Venezuelan President Nicolas Maduro labeled the incident as an act of terrorism.
The students were also protesting against the government's proposed constitutional assembly, which President Nicolas Maduro says will end the protests. The beleaguered president, who for weeks has been thundering about alleged coup attempts against him, said the helicopter was flown by a pilot who worked for a former minister.
Videos and photos shared on social media Tuesday night showed a police helicopter scientific flying over Caracas. He said in the video he represented a coalition of military, police and civilian officials opposed to the "criminal" government, and urged Mr Maduro's resignation and called for general elections.
His "fight" was not against security forces, but "against the impunity of this government. It is against tyranny".
How the country navigates the current crises would do a lot to settle fears of political upheaval in the nation.
No one was injured in the incident, which came amid yet more turmoil in the country as the chief prosecutor, Luisa Ortega Diaz, was stripped of some of her powers, and opposition politicians were shoved and harangued by pro-government colleagues inside the National Assembly.
Maduro warned earlier this week he is willing to do whatever it takes to defend Chavez's revolution, even if it means using arms. Nobody was hurt in the attack, and there was no indication Wednesday of any widespread rebellion in the armed forces or government agencies.
Over the previous three months, the 54-year-old socialist leader had faced protests from opposition leaders who decried him as a dictator who had wrecked a once-prosperous economy. By Tuesday evening, however, it appeared that Maduro's government remained in control.
During an interview with state television VTV, El Aissami said "despite the adverse climate conditions our Bolivarian National Army have found the helicopter used yesterday in two terrorist attacks against institutions".
"It can not be called anything other than terrorism", added Moreno, following an inspection of the site, located about a kilometer from the presidential headquarters.
In a video circulating on social media, the commander of a national guard unit protecting the legislature aggressively shoved National Assembly President Julio Borges as he was walking away from a heated discussion.