Torkil Tyvold, an executive with mining and energy company Norsk Hydro, was last seen on May 25th leaving his apartment building in Rio de Janeiro's Ipanema neighbourhood "in the direction of the beach," the company said.
Police are investigating the possibility of drowning, local media reported.
Tyvold, who is 59, is the company's project director in Brazil.
Norsk Hydro said it was doing everything in its power to support the search and that "officials, friends and volunteers" in Rio were distributing pamphlets with Tyvold's photo.
The company said it was "too early" to say what might have happened to the executive.
Norsk Hydro has owned Brazilian mining company Hydro Alunorte since 2011.
The Norwegian multinational has operations in more than 40 countries.