At least seven vehicles were torched in the capital and Mymensingh on Sunday leaving 10 people injured.
It is unclear who are responsible for the arson.
The incidents took place shortly after police embargoed gatherings in Dhaka after the ruling Awami League and the BNP planned parallel programmes to celebrate and protest the anniversary, respectively.
In Dhaka, five buses were set ablaze near the Baitul Mukarram National Mosque, Tejgaon, Gendaria, in front of the Jamuna Future Park, and Gulistan.
Around evening, a private car was torched at Shanir Akhrha.
No casualties have been reported.
Meanwhile, a bus was set ablaze in front of the Mymensingh Medical College and Hospital around Sunday noon, injuring at least 10 people.
The injured have been hospitalised.
Tension is running high after police locked the BNP's headquarters and barred Khaleda Zia from leaving her Gulshan office since Saturday.
She has reportedly told her supporters to go ahead with planned agitations.
Khaleda said she would get out of her office and join street protests.