The deadly toxic gas attack, and the pictures of dying children that accompanied it, led US President Donald Trump to launch a missile attack on the Syrian airbase where the weapons are believed to have originated.
Mr Johnson made his sanctions threat as he arrived in Italy on Monday in a bid to persuade G7 leaders of the case for tougher action against Russia.
He said: “We will be discussing the possibility of further sanctions certainly on some of the Syrian military figures and indeed on some of the Russian military figures who have been involved in co-ordinating the Syrian military efforts and are thereby contaminated by the appalling behaviour of the Assad regime.”
The US and EU currently have a range of sanctions against Russia related to Mr Putin’s annexation of Crimea three years ago.
While the sanctions are believed to have had an impact on the Russian economy, with Moscow’s diplomats lobbying to have them lifted, they have not forced Mr Putin to heel in Ukraine.
There was outrage across the world after dozens of civilians were killed in what is believed by the West to have been a chemical weapons attack on the Syrian village of Khan Sheikhoun by the Assad regime.
Russia and Iran have issued a joint call for an “unbiased investigation” into the incident, which provoked Mr Trump to launch 59 Tomahawk missiles at the airfield in Syria’s Homs province.
Foreign Minister Sergei Lavrov and his Iranian counterpart Mohammad Javad Zarif agreed to call for the probe on Monday, while denouncing the US attack on the Syrian airbase as “an act of aggression against a sovereign nation”.
Russia has argued that the chemicals were released after the Syrian air force undertook an attack on the outskirts of the village in a bid to destroy militant facilities used to produce chemical bombs, though the claim has been dismissed by the US as “simply not credible”.