The three men and two women were detained near Nakkapalli in Visakhapatnam district on Wednesday on suspicion after Odisha Police alerted their Andhra counterparts.
They allegedly fled from a hotel in Bhubaneswar on Monday when the staff sought proof of their identity, raising suspicion.
The foreigners were in a car with Delhi registration number which did not stop at a toll gate in Andhra Pradesh. Police then chased the car and intercepted them.
Visakapatnam Superintendent of Police K. Praveen said they all had valid passports, visas and other documents. They had visited various parts of the country before entering Andhra from Odisha.
All of them are from Tehran. While two of them came to India on December 28, the other three came on January 12, informed sources said.
Meanwhile, Odisha Inspector General of Police (Crime Branch) Arun Bothra said: "It is almost confirmed they are not terrorists."
But he added that their "unusual behaviour" in Bhubaneshwar was being examined. Police sources said the Iranians would be allowed to continue with their travel plans if nothing untoward was discovered.
Security forces in and around Viskhapatnam are on high alert in view of the international fleet review beginning on February 4.