Life-size cutouts of BJP president Amit Shah, who is here to attend the party's national executive meeting, were found torn and defaced at Power House Chhak area.
Cutouts of Prime Minister Narendra Modi were, however, left untouched.
"It is an unfortunate incident. We condemn it as such an act is against the culture and tradition of Odisha," Senior BJP leader Suresh Pujari said.
Pujari accused ruling BJD activists as being behind the incident and said that the party's leaders were worried over BJP's surge in Odisha.
Some other BJP leaders too claimed that the incident is the work of their political rivals.
Police are, however, yet to find the culprits.
Rejecting the allegations, BJD Spokesperson Dibya Shankar Mishra said "BJD does not believe in such vandalism."
Some senior BJP workers have expressed disappointment over the absence of cutouts of former Prime Minister Atal Bihari Vajpayee and party veteran L K Advani.
BJP's two-day national executive meeting will begin here today with all party bigwigs including Prime Minister Narendra Modi joining the deliberations.