The Labour leader said the action makes real accountability for war crimes less likely.
Britain should not be taking instructions from Washington and putting British military personnel in harm’s way, Mr Corbyn said.
“Bombs won’t save lives or bring about peace,” he said.
Mr Corbyn added: “This legally questionable action risks escalating further, as US defence secretary James Mattis has admitted, an already devastating conflict and therefore makes real accountability for war crimes and use of chemical weapons less, not more likely.”
His response follows the launch of missile strikes by the US, UK and France overnight.
Three waves of strikes destroyed important infrastructure at sites connected with the Syrian regime’s chemical weapons programme.
British Tornado GR4s departed from RAF Akrotiri in Cyprus and fired Storm Shadow missiles at a military facility near Homs, where the regime is said to have kept chemical weapon precursors.
Other sites near Damascus were also targeted in the assault which US Defence Secretary Jim Mattis called a “one-time shot”.
Mr Corbyn added: “Britain should be playing a leadership role to bring about a ceasefire in the conflict, not taking instructions from Washington and putting British military personnel in harm’s way.
“Theresa May should have sought parliamentary approval, not trailed after Donald Trump.
“The Government should do whatever possible to push Russia and the United States to agree to an independent UN-led investigation of last weekend’s horrific chemical weapons attack so that those responsible can be held to account.”