The incident happened near the Government Hospital Square when Patnaik was returning to Bhubaneswar after attending the foundation stone laying ceremony for the Rs 331-crore heritage corridor project in the temple town.
The BJP activists also showed black flags as Patnaik's cavalcade passed by.
Earlier, three members of BJP-backed Bharatiya Janata Yuva Morcha (BJYM) and Congress-affiliated NSUI were taken into custody for waving black flags at Patnaik on Bada Danda (Grand Road) in Puri, sources said.
"Our activists under the leadership of Jayant Das have hurled eggs, targeting the chief minister's convoy. This protest will continue till Patnaik takes action against some of his tainted ministers," BJYM state president Irasish Acharya told reporters in Bhubaneswar.
Later, the opposition activists also sprinkled cow-dung water on the Grand Road in front of the Jagannath temple to "purify" it, claiming that the "tainted" state ministers, who attended the foundation stone laying ceremony there, made the sacred path "impure".
Eggs were also hurled at the convoy of Parliamentary Affairs Minister BK Arukha near Malatipatapur on the outskirts of the city. The opposition parties have been protesting for weeks, demanding the removal of the Minister of State for Home DS Mishra for his alleged involvement in the Kalahandi woman teacher's kidnap and murder case.
Police were not immediately available for comments on the attack on the chief minister's convoy.
With PTI inputs.