Explosions hit the capital, Damascus, as well as two locations near the city of Homs, the Pentagon said.
Russia's ambassador to the US responded by saying the attack on its ally "will not be left without consequences".
"The nations of Britain, France, and the United States of America have marshalled their righteous power against barbarism and brutality," US President Donald Trump said in an address from the White House at about 21:00 local time (02:00 BST).
"The purpose of our actions tonight is to establish a strong deterrent against the production, spread, and use of chemical weapons," he said.
The wave of strikes is the most significant attack against President Bashar al-Assad's government by Western powers in seven years of Syria's civil war.