"An air commodore was among the four soldiers killed," the Syrian Observatory for Human Rights said.
"The airbase was almost completely destroyed -- the runway, the fuel tanks and the air defences were all blown to pieces," the Britain-based monitoring group said.
"There were Sukhoi-22, Sukhoi-24 and MiG-23" fighter aircraft on the ground, Observatory chief Rami Abdel Rahman told AFP.
The officers' quarters at Shayrat, the government's second most important airbase, were also damaged, he added.
Washington said that Russian military officials in Syria were informed of the strike beforehand in order to avoid casualties that could prompt a broader crisis.