He said: "The enemy is blocking and besieging large cities and not allowing residents to leave the city, not giving a chance to deliver food, and flying enemy bombs from above that sow death."
UN sources said on Saturday that at least 351 civilians were killed and 707 others were injured in Ukraine.
A humanitarian corridor is a type of temporary demilitarized zone intended to provide safe passage for victims of conflict and for humanitarian agencies to reach those affected by the crisis.
The Major Archbishop wrote, "I would especially like to address the international community. We must not remain silent. Let us do everything possible so that at least humanitarian convoys can reach the cities that are in the hands of the unfortunate enemy." in an appeal.
"When the enemy bombs cities, many buildings quickly turn into cold traps with no heat, no light, no water. We must help them somehow, but the enemy does not allow our help to reach the needy."
The Archbishop drew attention to the situation in the cities and towns in the north, east and south of Ukraine, where they are facing the onslaught of a Russian offensive that began on the night of 24 February.
On Friday night, Kharkiv, the country's second largest city, faced airstrikes and shelling amid 20 cm of snowfall, he said. He also drew attention to the hopeless situation in Sumy, Mariupol and Volnovakha.
"Humanitarian corridors can be built!" Archbishop Shevchuk said. "Have green corridors of life so that peaceful populations can move to safer places, and humanitarian convoys can bring food, warmth and human solidarity to those in need."
He explained that while Ukrainians were defending their land, they were also praying and serving others.
Archbishop Shewchu especially thanked the volunteers and various community organizations for reaching out to those in need. He said that each parish in the center, east and south of the country is turning into "centres of social service for our volunteers".