"It's a simple, informative campaign without calling for hysteria," defence ministry official Luiz Felipe Linhares said in a statement on Tuesday, Xinhua news agency reported.
The South American country is not a traditional terrorist target and the government hopes the initiative will reduce Rio's vulnerability to possible attacks.
The campaign involves the distribution of brochures, posters and booklets explaining how to identify people engaging in suspicious activity, officials said.
"Our country has never faced this type of threat so we need to make sure that people are more alert," Brazilian defence force anti-terrorism chief, Mauro Sinott said.
"The message that we want to pass on is that if you think a certain situation is suspicious, it is because it is in fact suspicious."
Earlier this month the government said Brazil's intelligence agencies were working alongside counterparts in the US, Britain, France, Israel and Russia to counter the threat of terrorism.
Brazil will also deploy tens of thousands of troops in Rio's streets to ensure the safety of athletes, officials, residents and an estimated 600,000 foreign visitors during the August 5-21 Games.
In total, there will be 85,000 security personnel - including armed forces, police and security agents - patrolling the city.