Of those, 11 have symptoms of flu or conjunctivitis, though nobody is seriously ill, the National Public Health Service for Wales said.
"We believe the risk to the health of the general public is low," said Doctor Marion Lyons, the NPHS lead consultant in communicable disease control.
The outbreak of the H7N2 low pathogenic avian influenza strain -- different to the most virulent H5N1 strain -- was confirmed Thursday on a farm in north Wales near the town of Corwen.
Fifteen Rhode Island Red chickens died and a further 30 birds have since been slaughtered.
Results from tests at the farm are yet to be released.
"Person-to-person spread would be very unusual but limited spread of this type has been seen elsewhere in the past in some cases of bird flu," Lyons said.
The people defined as having had possible contact with bird flu had been in contact with infected poultry or the affected premises, plus those who have had close contact with another person with confirmed or suspected avian influenza.
"Of the people with conjunctivitis or a flu-like illness, some did not have close contact with infected poultry," Lyons said.
Four people have so far tested positive for bird flu and a further four are being treated as having had the disease.
The last case of bird flu in Britain was an outbreak of H5N1 in February at a turkey plant in eastern England.
Nearly 160,000 turkeys were culled as a precaution in the country's first major outbreak of the potentially lethal virus.
The H5N1 strain of bird flu has infected at least 306 people worldwide and killed around 185 of them, mostly in southeast Asia, since the end of 2003, according to World Health Organisation figures.