Lesley Griffiths said the risk would not fall in coming weeks, and spring wild bird migration could increase the chances of further cases.
On Monday it was confirmed that a wild duck died from the disease in Conwy, following cases in south Wales.
On Tuesday, Ms Griffiths told AMs that more cases were likely to be found.
Public health officials have stressed that the risk to humans is "very low".
Ms Griffiths previously announced the extension of an all-Wales avian flu prevention zone until 28 February 2017.
Similar measures have been introduced in England, Scotland and Northern Ireland.
"Work is in hand, with Defra and the Scottish Government, to consider what the exit strategy might be for lifting the prevention zone," she said in a statement.
"I cannot stress enough the need for those who keep poultry flocks and other domestic birds to remain alert for signs of the disease, to contact their private veterinarians if they have any concerns and to practice the highest levels of biosecurity," Ms Griffiths added.
The risk of more cases of avian flu in poultry and other captive birds may increase in the weeks ahead, Wales' rural affairs secretary has warned.