The measure drafted by Britain, France and the United States won nine votes in favor at the Security Council while three countries opposed it -- China, Russia and Bolivia. Kazakhstan, Ethiopia and Egypt abstained.
UN resolutions require nine positive votes and no veto to be adopted.
It was the seventh time that Russia, Syria's top military ally, has used its veto power to shield the Damascus regime.
China, also one of the five veto-wielding permanent members of the Security Council, has joined Russia in vetoing six resolutions on Syria.
Russian President Vladimir Putin had warned that imposing sanctions on Syria during ongoing peace talks in Geneva was "completely inappropriate" and would undermine the effort to end Syria's nearly six-year war.
"This resolution is very appropriate," US Ambassador Nikki Haley told the council after the measure was defeated in the vote.
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"It is a sad day on the Security Council when members start making excuses for other member states killing their own people."
"The world is definitely a more dangerous place," she said.
The resolution would have put 11 Syrians, mainly military commanders, and 10 entities linked to chemical attacks in 2014 and 2015 on a UN sanctions blacklist.
The measure followed a UN-led investigation which concluded in October that the Syrian air force had dropped chlorine barrel-bombs from helicopters on three opposition-held villages in 2014 and 2015.
The joint panel of the United Nations and the Organization for the Prohibition of Chemical Weapons (OPCW) also found that Islamic State jihadists used mustard gas in an attack in 2015.
The vote marked the first major council action by the new US administration, which is seeking warmer ties with Russia.
The Syrian government has repeatedly denied using chemical weapons in the war that has killed 310,000 people since March 2011.