Journalists dived for cover in the equestrian press office in Deodoro when a bullet pierced the large tent.
The bullet reportedly came with two metres of New Zealand team official who was left "visibly shaken".
The bullet, identified locally as a 5.56mm assault rifle round, landed near the space set aside for press conferences.
The bullet is believed to have been fired from an assault rifle
Police also carried out a controlled explosion on a bag left in the street near to the elite cycling route also on Saturday amid more chaotic scenes in Brazil.
A small hole could be seen in the roof of the tent where the bullet came through.
There are unconfirmed reports the bullet could have come from a military base located next to the equestrian centre in Deodoro in Rio.