He told the BBC’s Andrew Marr Show that it was right to ask whether Russian forces had deliberately targeted civilians.
Eighteen lorries and a warehouse were destroyed and 20 people killed in last Monday’s attack.
Russia denied responsibility, blaming rebel shelling or a US drone.
Mr. Johnson also said Russia was “guilty of protracting” the war in Syria and of “making it far more hideous”.
His comments came as Aleppo sustained heavy bombing, with the Syrian government saying it had launched an offensive to retake rebel-held areas.
In the latest fighting, rebel forces in the city were reported to have retaken the Palestinian refugee camp of Handarat, on elevated ground north of the city.
The strategic area fell to government troops on Saturday.
The UN Security Council is due to meet on Sunday morning in New York to discuss Aleppo.
The meeting was requested by the US, the UK and France.
United Nations special envoy Staffan de Mistura described last week’s attack, on an aid convoy and Syrian Arab Red Crescent warehouse outside Aleppo, as an “outrage”. The US said two Russian warplanes were involved in the attack.
Mr. Johnson appeared to go further, saying the convoy could have been deliberately targeted.
Russian President Vladimir Putin was “not only… handing [Syrian President Bashar] Assad the revolver”, he told the BBC’s Andrew Marr programme. “He is in some instances actually firing the revolver himself.
“We should be looking at whether or not that targeting is done in the knowledge that those are wholly innocent civilian targets. That is a war crime.”