Saturday's violence threatens to unravel a humanitarian deal for Homs which was the first concrete result of talks launched two weeks ago in the Swiss city of Geneva to try to end Syria's civil war.
The Syrian Arab Red Crescent said mortar bombs landed close to its convoy and shots were fired at its lorries, wounding one of its drivers, Al Jazeera reported.
At least nine Red Crescent and UN vehicles were trapped in Homs for several hours after dark when the explosions struck, but the team managed to leave shortly before 10pm local time (20:00 GMT), leaving two damaged lorries.
"Although the team was shelled and fired upon, we managed to deliver 250 food parcels (and) 190 hygiene kits and chronic disease medicines," the Red Crescent said.
The UN says it wants to distribute food for 2,500 people, along with medical kits, bedding, cash and other support for those leaving or those choosing to stay in the Old City.
Talal al-Barazi, the governor of Homs, told the state news agency SANA that aid was distributed to two neighbourhoods, Bustan al-Diwan and Hamidiyeh.
Video footage published by activists showed eight white cars with UN markings and a lorry stopped at a narrow street corner strewn with rubble.