The newspaper, citing a federal government official close to the ruling United Russia party, said the authorities were irritated by Guriev's support of Navalny, for whom Guriev wrote a letter of recommendation to attend a program at Yale University in 2010.
Navalny, one of the most visible figures in the mass protests against President Vladimir Putin's rule, is currently on trial on embezzlement charges that his supporters say are politically motivated.
Guriev has headed the New Economic School, one of the most prestigious economic institutions in the country, since 2004. The school's board of directors includes Deputy Prime Minister Arkady Dvorkovich.
The school has not yet confirmed his resignation, and Guriev made no immediate comment about the matter, which was also reported by Kommersant and Prime news agency. Guriev is currently in France, where his family lives.
Prime, citing a source in academic circles, said “important events” influenced Guriev's decision to leave, but did not elaborate.
Guriev, an outspoken commentator and regular fixture at major investment conferences, has come under official scrutiny in recent weeks. Investigators with the Investigative Committee questioned him last month in connection with the politically tinged case into the Yukos oil company. Tax authorities also visited the school's premises around the same time, according to the New Times magazine.
As an expert for the Kremlin's human rights council, Guriev took part in an evaluation of the court proceedings against former Yukos CEO Mikhail Khodorkovsky, concluding that he was sentenced unjustly.
The Investigative Committee said Wednesday that Guriev was questioned about the Yukos case a month ago, Interfax reported.
A source close to the school told The Moscow Times that problems were connected to Guriev personally and not to the school itself. He refused to comment further and demanded anonymity, saying he did not want to draw unwelcome attention to himself.
But Pavel Salin, director of the Moscow Financial University's Center for Political Research, said that the tax authorities' visit to the school suggested that Guriev's situation was not “purely political.”
Separately, Guriev on Tuesday declined to run for a seat on the board of directors at Sberbank, the nation's biggest lender. He asked Sberbank to exclude him from the list of candidates, saying his decision was motivated by “personal reasons” and no one had put any pressure on him, Vedomosti reported.
Asked whether he was aware of the situation, President Vladimir Putin's spokesman Dmitry Peskov told Vedomosti that Guriev's whereabouts were his “own personal matter.”
The development came a day after Guriev's former colleague from the New Economic School, Igor Fedyukin, resigned as deputy education and science minister, citing “unprecedented pressure” from the ministry.