Ambulances and firefighters were called to the scene after a smell of smoke was reported shortly after 15:30 BST.
A generator that was inside a marquee has been turned off.
A spokesman for the Northern Ireland Ambulance Service said up to 40 people were being checked but no-one appeared to have become seriously ill.
"Nobody has been taken to hospital yet and we're not sure that anyone actually will [need] to be taken to hospital," John McPoland added.
He said firefighters called for ambulance staff at about 16:00 BST after a number of people at the circus complained of feeling unwell.
"We responded with three rapid response paramedics, one of our HART (Hazard Area Response) teams, two A&E crews and a patient care vehicle.
"The first paramedic on the scene gave us a situation report that no-body seemed too seriously ill as a result of the incident, and he just wanted further personnel there to help him check everybody out," Mr McPoland said.

Ismail Morinaj was detained after giving an interview in which he admitted carrying a gun for protection.
Last year's match had to be abandoned as Serbian fans invaded the pitch and attacked Albanian players.
Security for the Serbia team is high in Albania before Thursday's match.
Although the match will take place in Elbasan, an hour's drive to the south-east of Tirana, the Serbia team are staying at a hotel in the capital surrounded by police.
As the team bus arrived in Tirana, stones were thrown and a window was cracked. Serbian media reported that Albanian officials had refused to receive a note of protest from Belgrade, insisting nothing had happened.
Reports from Tirana spoke of roads inside the city being closed amid a major police operation.
Albania are third in their Euro 2016 qualifying group, behind Portugal and Denmark, but far ahead of Serbia and still hoping to qualify for the knock-out stages of the competition.
Police arrested the 33-year-old suspect and three other men, saying they had found a Zastava pistol and several cartridges, as well as 36 tickets for Thursday's match.
Tensions had already been high before the Euro 2016 tie at the Partizan Stadium in Belgrade and ordinary Albanian fans were not allowed to attend the match.
The two countries have had a long and bitter history of rivalry, and ethnic-Albanian-majority Kosovo's decision to declare independence from Serbia in 2008 brought relations to a new low.
Ismail Morinaj admitted flying the drone from a church across the road from the stadium. As it hovered above the pitch, a large "greater Albania" flag could be seen, portraying nationalist claims to neighbouring states.
Serbia defender Stefan Mitrovic snatched at the drone and fans poured on to the pitch, attacking Albania players.
The ensuing brawl and the decision to abandon the game prompted football officials to deduct three points from Serbia, and they stand at the bottom of their group in Euro 2016.
Only a few dozen Serb supporters will be allowed into the stadium for Thursday's match, which will have a heavy police presence.
"This is an opportunity to show our values in supporting the national team and hosting the guest team," said Albanian Interior Minister Saimir Tahiri.
Paramedics have treated a number of people for the effects of breathing in fumes at a circus in Carrickfergus, County Antrim.
[NEXT_CONCEPT]
A man who flew a drone into a football stadium in Serbia during a Euro 2016 qualifier last October has been arrested ahead of the return leg in Albania.