The teddy bears carried signs reading, "Belarus freedom" and "We support the Belarus struggle for free speech," according to a USA Today
The toy bears descended over the town of Ivyanets, near Minsk, a Swedish news agency reports.
The stunt was promoted free of charge by a Swedish ad agency on behalf of the pro-democracy group Charter 97.
The plane flew from Lithuania, according to the local newspaper. In a note it called a "legal warning and disclaimer" on its website, Studio Total acknowledges that violating military space "of a dictatorship" involves "real danger."
The entire campaign was paid for by Studio Total. "The airplane we flew in was our own, and we piloted it ourself. We do not support breaking of international law. But when it really comes down to it, the only law you should follow is your heart."
Belarusian air defense forces earlier denied that a Swedish plane had invaded its airspace and successfully dropped the teddybears over the country, calling the story a provocation.
But now, the story has changed.
"How can you explain that a light aircraft, which not only crossed the border, but also with impunity, invaded the territory of the Republic of Belarus? It is first and foremost a matter of the safety of our citizens," Lukashenko said at meeting Thursday on the modernization of the armed forces, according to news agency Interfax.
Lukashenko says the perpetrators will be punished, as well as some members of the military, border and security forces who allowed the plane to fly deep into the country.
Belarusian authorities continue to hold a young independent Belarusian journalist, Anton Suryapin, who was arrested for posting pictures of the teddybears, some dangling from trees, on the Internet, the BBC reports.
Lukashenko has been president of the former Soviet republic since 1994. In 2005, Secretary of State Condoleezza Rice described Belarus as "the last true remaining dictatorship in the heart of Europe."