The two journalists, Øystein Bogen and Aage Aune from TV2, were arrested three times and detained for several hours, during which time their phones and other communications equipment were confiscated.
Bogen was then accused of taking drugs and asked to take a test.
Russia's Foreign Ministry conceded that local law enforcement officials had carried out "a series of unwawanted actions towards the citizens of Norway".
"In this regard we apologise to Mr Bogen and Mr Aune. The current situation will undoubtedly be worked out in detail and those gulty will receive the corresponding punishment."
"We would like to assure you that the authorities of the Russian Federation will take all necessary measured to avoid the repetition of similar cases in the future."
Bogen said he had never seen such levels of harassment in nearly 20 years of reporting in Russia.
"I have worked as a journalist for TV2 in Russia since 1995. I have never experienced anything similar. It has been pure harassment," he told TV2. "Ordinary Russians fear their own police. Now I realize that we also have reason to be afraid. In a society where the police do not follow the law, where they evidence from thin air, it's not safe."