Berezovsky, who lives in London, became a member of the academy in 1991 and, despite being convicted of embezzling $43 million from a leading Russian bank, still receives a monthly salary of 10,000 rubles ($420), which will be increased to 25,000 rubles ($1,060) in June.
"If criminal proceedings are launched against a corresponding member of the Academy of Sciences, he must appear in court and prove the charges are mistaken. And if he fails to do so, he should be expelled," Strakhov told a general meeting of Academy members.
Strakhov wants amendments made to the Academy Charter to ensure that members convicted of a criminal offense by a court are stripped of their lifetime membership.
Twelve criminal investigations have so far been launched in Russia against Berezovsky, a one-time close associate of the late president Boris Yeltsin, and he also faces a criminal probe in Brazil.
A former chief investigator also claimed last month that Berezovsky was behind the murder of investigative journalist Anna Politkovskaya.
The Kremlin has repeatedly urged Britain to extradite Berezovsky, for plotting to stage a coup against Vladimir Putin, the then-president and current prime minister.
The allegations came after an interview with The Guardian newspaper last April where Berezovsky said: "We need to use force to change this regime...It isn't possible to change this regime through democratic means. There can be no change without force, pressure."
