Reports of places hit by strikes include a military airfield in the centre of Caracas, La Carlota and the main military base of Fuerte Tiuna.
Several of the surrounding communities are without power.
Videos of explosions and helicopters flying overhead have been circulating on social media but have not yet been verified.
Journalist Vanessa Silva, who lives in Caracas, told the BBC that she heard a huge explosion “stronger than thunder”, causing her home to vibrate.
“My heart was pumping and legs were shaking,” she said.
The Venezuelan government said the states of Miranda, Aragua and La Guaira were also hit, and that the strikes aimed to seize Venezuela’s oil and minerals.
It said in a statement that it “rejects, repudiates and denounces before the international community the extremely serious military aggression perpetrated by the current Government of the United States of America”.
Cuba and Colombia have also denounced the attacks.