Kasparov said police at Moscow's Sheremetyevo airport took his passport and ticket, preventing him from boarding the plane.
"Police at the airport have simply stolen our passports," he told Ekho Moskvy radio. "They refuse to return them and have given no grounds."
Another opposition leader, Eduard Limonov, said he also was barred from the flight.
"Clearly the purpose is to prevent Garry and Limonov from making it to the march," Kasparov aide Marina Litvinovich said from an airport waiting area.
Kasparov is a vocal critic of President Vladimir Putin and leader of an opposition movement that has helped organize a series of so-called Dissenters' Marches, several of which were violently broken up by police. He had planned to take part in an afternoon anti-government protest in Samara, on the Volga River, scheduled to coincide with a Russia-EU summit that began Thursday evening.
A correspondent for The Wall Street Journal, Alan Cullison, said he and at least one other Western journalist had missed the flight because their passports and tickets were being withheld. He said police told them there was a potential problem with the tickets.
The summit participants include Putin and German Chancellor Angela Merkel, whose country holds the rotating EU presidency. With EU concerns about Russia's record on democracy and human rights among the many issues shadowing the meeting, Germany has urged the Kremlin to allow the rally Friday, and authorities in Samara have given approval for a demonstration.
Merkel voiced concern at the conclusion of the summit Friday about the activists having problems traveling to the site.
"I'm concerned about some people getting problems in traveling here. I hope they will be given an opportunity to express their opinion," Merkel said.
But activists said they were being harassed even before the summit.
Kasparov said Thursday that police detained an activist at the Samara airport. About 15 others also were detained at least briefly, said Anastasiya Kurt-Adzhiyeva, a coordinator for Other Russia, an opposition umbrella group that includes Kasparov's United Civil Front.
In the past few weeks, "police have been terrorizing (those involved in the march), putting psychological pressure on them," United Civil Front spokesman Denis Bilunov said in Samara.
"Unfortunately, the law enforcement organs are acting like they don't know this (protest) action has been authorized by officials," he told reporters.
Sergei Kurt-Adzhiyev, the editor of the local edition of liberal newspaper Novaya Gazeta, said he was summoned by prosecutors for questioning Friday in connection with the preparations for the Dissenters' March. Earlier, investigators seized computer hard drives from the newspaper's editorial office, he said.
Bilunov said Kasparov and other Dissenters' March organizers were still hoping to fly to Samara on Friday.
After the morning flight departed, Kasparov, Limonov and others were still being kept in a waiting room, and their passports had not been returned, Litvinovich said. Limonov is former head of the outlawed National Bolshevik Party.