The crossover to humans is likely to fuel public fear of bird flu, especially since the H7N2 strain is known to be less virulent than the deadly H5N1, and therefore was presumed less likely to spread between species.
A further nine people are currently experiencing flu-like symptoms or conjunctivitis following contact with birds infected with the H7N2 strain, the Welsh Assembly Government said.
The National Public Health Service for Wales (NPHS) has received microbiological test results from eight people of the 36 identified as having had contact with the virus.
"The illness people are experiencing is, for the most part, not serious.
No one is seriously ill," it said.
Prelimary tests have, so far, not ruled out the spread of the virus between humans.
"For this reason, the NPHS is contacting every individual who has been in close contact with the people who are cases," the Welsh Government said.
"People identified as contacts are being offered medication to reduce the severity of any impact from the infection."
Marion Lyons, lead consultant in communicable disease control for the National Public Health Service for Wales, said she believes the risk to the general public is low.
"Avian flu is primarily a disease of birds," she said.
"H7N2 is different to and very mild compared with H5N1.
"Investigations also show that, when it spreads from person to person, the illness experienced becomes milder."
Meanwhile, the investigation into the source of the outbreak has confirmed that the 15 chickens believed to have infected the farm were purchased from Chelford Market, Cheshire.
Christianne Glossop, chief veterinary officer for Wales, said Chelford Market is one line of inquiry Animal Health are following in the ongoing investigation.
"As part of the tracing exercise, I would urge anyone, who has not already been contacted by Animal Health officials, and who has purchased from or supplied to Chelford Market in Cheshire on Monday 7 May 2007 or any poultry keeper who visited Chelford Market on this date whose birds have subsequently become ill to contact their local Animal Health Office or the Defra helpline," she said.
The outbreak is the second of this year, and the first time the infection has passed to humans in the UK.
In February, an outbreak H5N1 virus on a Suffolk farm, owned by Bernard Matthews, killed some 2,600 birds with another 159,000 being slaughtered.
The strain was linked to an almost identical strain found in an outbreak in Hungary in January.
Since 2003, a total of 307 humans worldwide have been infected with the H5N1 virus, with 186 cases ending fatally, according to World Health Organisation (WHO) statistics published in May 2007.