The violence on Friday highlighted the task facing an unprecedented force of 85,000 soldiers and police deployed to secure the Olympics.
Rio police said in a statement that a man was mugging people near the Maracana stadium when he was intercepted by one of the police officers sent from another area of Brazil to Rio as part of the huge reinforcements.
“The man was carrying out assaults when a military police officer… shot him,” the statement said.
Hours earlier, an architect was killed while driving by one of the main entrances to the Olympic Boulevard, a redeveloped port area that now hosts the Olympic flame and has become a major tourist attraction.
The woman, 51, was attacked by three armed muggers, police said. She tried to flee and was shot in the head.