President Donald Trump announced the extraordinary night-time operation on social media hours after the attack.
Explosions rang out and low-flying aircraft swept through Caracas, the capital, as Maduro's government accused the US of attacking civilian and military installations.
It was not immediately clear who was running the country, and Maduro's whereabouts were not immediately known.
Under Venezuelan law, the vice-president, Delcy Rodríguez, would take power.
There was no confirmation that had happened, though she issued a statement after the strike.
"We do not know the whereabouts of President Nicolas Maduro and first lady Cilia Flores," Rodriguez said.
"We demand proof of life."
Maduro, Trump said, "has been, along with his wife, captured and flown out of the Country. This operation was done in conjunction with U.S. Law Enforcement. Details to follow."
He set a news conference for Saturday morning.
The legal implications of the strike under US law were not immediately clear.
Republican senator Mike Lee posted on X that he had spoken with Secretary of State Marco Rubio.
Rubio told Lee that Maduro "has been arrested by U.S. personnel to stand trial on criminal charges in the United States".
Maduro was indicted in March 2020 on "narco-terrorism" conspiracy charges in the Southern District of New York.
The explosions in Caracas, Venezuela's capital, early on the third day of 2026 - at least seven blasts - sent people rushing into the streets, while others took to social media to report hearing and seeing the explosions.
It was not immediately clear if there were casualties on either side.
The attack itself lasted less than 30 minutes and it was unclear if more actions lay ahead, though Trump said in his post that the strikes were carried out "successfully".
The strike came after the Trump administration spent months escalating pressure on Maduro.
The CIA was behind a drone strike last week at a docking area believed to have been used by Venezuelan drug cartels - the first known direct operation on Venezuelan soil since the US began strikes in September.
For months, Trump had threatened that he could soon order strikes on targets on Venezuelan land following months of attacks on boats accused of carrying drugs.
Maduro has decried the US military operations as a thinly veiled effort to oust him from power.
Parts of Caracas remained without power, but vehicles moved freely.
Smoke could be seen rising from the hangar of a military base in Caracas, while another military installation in the capital was without power.
Venezuela's government responded to the attack with a call for people to take to the streets.
"The Bolivarian government calls on all social and political forces in the country to activate mobilisation plans and repudiate this imperialist attack," it said in a statement.
Maduro had "ordered all national defence plans to be implemented" and declared "a state of external disturbance".
It was not clear if the US Congress had been officially notified of the strikes.
Lawmakers from both political parties in Congress have raised deep reservations and flat-out objections to the US attacks on boats suspected of drug smuggling on boats near the Venezuelan coast, and the Congress has not specifically approved an authorisation for the use of military force for such operations in the region.
The US military has been attacking boats in the Caribbean Sea and the eastern Pacific Ocean since early September.
As of Friday, the number of known boat strikes is 35 and the number of people killed is at least 115.
They followed a major build-up of American forces in the waters off South America.
Trump has justified the boat strikes as a necessary escalation to stem the flow of drugs into the US and asserted that the US is engaged in an "armed conflict" with drug cartels.
