Ashokan and Harilal appeared before a court which remanded them in judicial custody till January 24.
On Wednesday, a group of 15 people stormed into the cabin of the SBI manager and vandalized it.
Santosh Karunakaran, the manager whose cabin was attacked, told the media on Thursday that the police had started their probe.
"A computer, two phones and a glass table top were damaged by the protesters. From now on the seniors in our bank will deal with this case," he said.
The police are on the lookout for 13 more people, including those attached to Left unions.
The SBI branch is located near Chief Minister Pinarayi Vijayan's office.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)