The Interfax news agency, citing unspecified police officials, said the suspect arrested Sunday was a son of a museum curator who had been in charge of the collection where the theft occurred until her death last October.
St. Petersburg police spokesman Vyacheslav Stepchenko said he could not comment on the reports.
Two other suspects, including the late curator's husband, reportedly were arrested last week, days after the thefts were made public, the AP reports.
The theft highlighted poor security at Russian cultural institutions, most of which suffered from funding cuts amid the country's post-Soviet economic troubles.
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Negotiations with Russia are possible if Moscow changes the goals of the special operation, the head of the Ukrainian Defence Ministry Oleksiy Reznikov said