Kaliganj police OC abdul Baten said pro-shutdown activists torched a bus on Wednesday morning at the Jamalpur market.
A covered van was set ablaze in the early hours of Wednesday at the Baghat area.
Locals and police later doused the flames.
Apart from these, there was no other reported incident of unrest in Gazipur.
Long distance buses have remained grounded but public transport in the city was reportedly normal.
Most of the public and private offices and business establishments remained open.
Joydebpur police OC SM Kamruzzaman said security personnel were posted at key points of the district.