After talks in Sochi, Macky Sall said the Russian leader had promised to ease the export of cereals and fertiliser, but gave no details.
Mr Putin denied Moscow was preventing Ukrainian ports from exporting grain.
Over 40% of wheat consumed in Africa usually comes from Russia and Ukraine.
But Ukraine's ports in the Black Sea have been largely blocked for exports since the conflict began. Kyiv and its allies blame Moscow for blockading the ports, which Ukraine has mined to prevent a Russian amphibious assault.
"Failure to open those ports will result in famine," the UN's crisis coordinator Amin Awad said in Geneva.
He said a grain shortage could affect 1.4 billion people and trigger mass migration.
The war has exacerbated already existing shortages in Africa caused by bad harvests and insecurity.
Food prices have shot up across the continent since Russia invaded Ukraine 100 days ago, pushing huge numbers towards hunger.
The head of the World Food Programme, Mike Dunford, said more than 80 million people were acutely food insecure, acutely hungry in Africa - up from about 50 million people this time last year.
Chad has declared a national food emergency. A third of the population needs food aid, according to the UN and the government has appealed for international assistance.
Mr Sall, who is Senegal's president, told Mr Putin he should be "aware that our countries, even if they are far from the theatre [of action], are victims of this economic crisis".
He said he was also pleading on behalf of other countries in Asia, the Middle East and Latin America.
Mr Putin said Russia was ready to guarantee the safe export of Ukrainian grain via ports on the Azov and Black seas it controls. He said the best solution would be to lift sanctions on Belarus, a close Russian ally, so the grain could be shipped that way.
Some analysts argue the Kremlin is hoping that a looming food crisis will put political pressure on the West by provoking big new refugee flows towards Europe from food-insecure countries in the Middle East and Africa.
Before Friday's meeting, Mr Putin said he was always on the side of Africa, but didn't explicitly mention the continent's food crisis.
Like many African countries, Senegal has avoided taking sides in the conflict and the Senegalese leader also said food supplies should be "outside" the West's sanctions on Russia. He said he had made this point when he spoke to the European Council earlier in the week.
Last Friday, US President Joe Biden dismissed the idea that the West bore responsibility for the global price rises.
"This is a Putin price hike. Putin's war has raised the price of food because Ukraine and Russia are two of the world's major bread baskets for wheat and corn, the basic product for so many foods around the world," he said.