The bullet landed on the floor of the press room after tearing through a canvas roof in Deodoro, the second largest Rio 2016 venue cluster, officials said, reports Xinhua.
New Zealand communications manager Ashley Abbott said the team's equestrian athletes were being contacted to inform them of the incident.
Press reports said New Zealand press attache Diana Dobson was left "visibly shaken", but physically unharmed.
The Rio equestrian centre is located next to a military base.
Officials said an investigation had been launched into the incident.
Meanwhile the Rio 2016 organising committee confirmed that a suspicious package was detonated at the Olympic cycle road race venue on Saturday.
"The security services found a suspicious package close the cycle road race finish line in Copacabana and as a precaution decided to perform a controlled explosion. There is no impact to the race which is ongoing," the spokesman said.
An official said the item was a small bag and that the police bomb squad's action was a precaution.
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