The measures are the first to take effect under the Caesar Act, which punishes any companies that work with Assad and seeks to prevent his normalisation without accountability for human rights abuses.
It also blocks US reconstruction assistance.
The first designations target 39 people or entities, including Assad and his wife Asma - the first time she has been slapped with US sanctions.
"The first batch of US sanctions against Syria under the so-called Ceasar Act reveals US violations of international laws and norms," said a Syrian foreign ministry statement, likening the behaviour of the US administration to that of "gangs" and "robbers".
It accused Washington of "hypocrisy" for justifying sanctions in the name of human rights.
US support for "terrorism" in Syria went against such principles, it added, referring to opponents of Assad's government.
"The tightening of sanctions against the Syrian people is a new dimension and form of this terrorism," said the statement released on the official SANA news agency.
Damascus warned earlier this month the sanctions would cause more suffering in a country already deep in economic crisis.
Syria's central bank on Wednesday devalued the pound after the currency depreciated for weeks on the black market in anticipation of the US measures.
US Secretary of State Mike Pompeo called the sanctions "the beginning of what will be a sustained campaign of economic and political pressure to deny the Assad regime revenue and support it uses to wage war and commit mass atrocities against the Syrian people."
Pompeo said the goal was to force Assad into accepting Security Council Resolution 2254 of 2015 - which called for a ceasefire, elections and political transition in Syria.
The European Union has imposed its own sanctions over Syria.
A French court separately on Wednesday convicted an uncle of Assad over money-laundering and misappropriation of government funds.
The Caesar Act is named after a former Syrian military photographer who fled at great personal risk in 2014 with 55,000 images of brutality in Assad's jails.
Follow us on Facebook, Twitter and Instagram to stay connected
