The man, whose name was not reported, was arrested on Wednesday afternoon near Gothenburg, Swedish news agency TT reported.
Police said the man used the online alias "bealarsson97" to meet the girls and then proceeded to harass them on a number of different chat rooms.
He convinced the girls to use the video chat website Skype, where he got them to pose in the nude and then threatened to publish the images online.
One of the girls committed suicide over the ordeal, officials said.
"What I can say is that the man is suspected of having published films on the Internet that caused problems for those affected," Orebro County Police spokesman Mats Nylen told the TT news agency.
Police said they believe there may be more victims.
"We believe there are more plaintiffs. There may be quite a few," Nylen said. "What's happened to this 13-year-old girl is tragically enough an alarm bell that shows how bad it can get."