The bullet landed close to one of the media tables at the end of the room where news conferences are held, leaving a clear hole in the roof.
"Obviously this is a worrying situation and is not an incident we can take lightly as the safety of everyone at our venue - athletes, horses, media and spectators - is of prime importance," FEI president Ingmar De Vos said in a statement.
"The Rio 2016 organizing committee have told us that the three authorities involved in security in Brazil, the military, civil police and national guard, have stated categorically that our venue was not the target, and that this incident has nothing to do with the games."
Andrada refused to speculate on where the bullet could have been fired from but said the entire competition venue is situated on military land."
As soon as we have information we will disclose that, especially where it comes from, why it got here and what kind of bullet it was," Andrada added.
"In the meantime, all the authorities have assured us that they have reinforced security around this area."
More than one source in the different security areas have emphasized that they have 100 percent assurance that it has nothing to do with the games and with the presence of the Olympic family and the press in this area.
"The incident came shortly after bomb-disposal experts blew up an unattended bag near the finish line of the men's road cycling race.
"We have to react to a global worry," Andrada said.
"We're not living in an easy moment so the authorities opted for the safe side. In a way it's good that they opt for the safe side, independently to the fact that this generates tension on the communication front. We'd rather have the security in perfect shape than the communications."I understand it was a backpack that someone forgot."
In the arena, William Fox-Pitt leads after the first day of the eventing competition, just 10 months after being put into an induced coma following a fall.Fox-Pitt, who only returned to competitive action in early April, rode Chilli Morning to a score of 37.
Christopher Burton of Australia and Santano II are second, 0.6 penalties behind the Briton, with reigning Olympic individual champion Michael Jung third with 40.9 aboard Sam FBW.Germany, which is bidding for a third straight Olympic title, leads the team competition, with Australia second and Britain third.
Meanwhile, a bomb squad is investigating after an apparent blast shook the area near the finish line of the men's cycling road race.
Herald columnist and Sky commentator Scotty Stevenson tweeted that it was "a controlled explosion. Suspicious package. Military have secured area".
Reporters could hear a loud boom on the press tribune and felt the ground shake as the cyclists had about 70km to go this morning.
A half dozen military police were cordoning off the area.
No one was immediately evacuated, and it did not appear that anyone was injured. The race was continuing and had not been rerouted.
