More than 148 people were killed in the bomb blasts at bus stations, hospitals and a power station in the cities of Jableh and Tartus, two strongholds of President Bashar al-Assad's regime.
Ban "condemns the terrorist attacks today that claimed the lives of dozens of civilians in the Syrian coastal cities of Jableh and Tartus," said his spokesman Stephane Dujarric.
He expressed "great concern of the escalating military activity in many areas in and around Damascus", particularly in Daraya, Aleppo and Idlib and in northern Homs, especially Al-Houla, he added.
Barrel bombs are indiscriminate weapons typically dropped from helicopters. Their use in Syria's war has come under fierce criticism by rights groups but the regime denies using them.
Ban renewed his call to all warring factions to spare civilians and said those responsible for such attacks must face justice.