Erik Skutle, 24, apologised on Thursday evening for what he said was a "serious breach of trust".
"I have today admitted to the police that I have smoked cannabis. I'm now awaiting what further actions the police will take as a consequence of the offence," he said. "What I have done is serious and I understand that there are consequences. I'm going to resign from all party posts, but will try to build up trust again slowly but surely."
He also apologised to his supporters both in and outside the party.
"I have betrayed those who helped me and supported me in my work in recent years," he said.
Skutle's statement came as a contrast to his previous statements on Wednesday, when he called for Norway to liberalize its policy towards cannabis, telling the VG newspaper that he believed the drug should be sold in pharmacies and state-owned off-licenses.
"I'm not saying that drugs are completely safe. Of course ... they are harmful. Nobody doubts that," he said. "But I think we have a better chance of controlling and reducing
consumption if we sell them over the counter, rather than having a total ban."
Skutle came under suspicion following a raid by police earlier this month on seven schools in his home city of Bergen, which saw more than 40 arrested.
During the raid, police found nine kilograms of cannabis in the boot of one 21-year-old's car. Skutle was brought in for questioning on Thursday with two other men, all of them suspected of involvement in cannabis-smoking.
Police lawyer Marita Weimar told Norway's NRK channel on Thursday that the three men were also suspected of cocaine use.
"All have been charged with possession and use of drugs. It's marijuana, and in addition to the other stuff, they also suspected to have used harder substances like cocaine," she said.
Skutle has been standing representing the constituency of Prime Minister Erna Solberg since she took the helm of the government in October 2013.