The company which runs the sites, Avara Foods, told the Yorkshire Post that an investigation was underway to find out the source of the H5N8 infection.
The second farm affected is thought to be geographically close to the initial case in the county, which was confirmed as Sowber Hill Farm at Newby Wiske, near Northallerton.
Though the farm is owned and run by the Willis family, the turkey rearing operation is contracted to Northamptonshire-based Avara Foods.
The second farm has not been named but it is also contracted to Avara Foods.
More than 10,000 birds have been culled.
Earlier this week, a 3km exclusion zone was put in place around Sowber Hill, and security personnel could be seen at the farm. Unauthorised personnel are now banned from entering the premises.
Poultry keepers in the area will now be expected to strengthen their biosecurity measures and a housing order - which requires anyone who owns free-range birds to keep them indoors is expected to be announced this week.
An Avara Foods spokesman said: “Avian Influenza (H5N8) has been confirmed on a turkey farm complex within the Avara Foods supply chain. We can confirm that all birds on site will be humanely culled and the complex will undergo intensive cleaning and disinfection, as per APHA regulations.
“Investigations to identify how the virus established itself onsite are ongoing.
“We have enacted our contingency plan and are working closely with government agencies and our wider suppliers and farming operations to manage this incident effectively and ensure that supply is not disrupted.
“Additional precautionary measures are in place across our agricultural operations, but it is important to stress that there is no risk to human health or food safety.”
On the discovery of the first Yorkshire case this week, UK chief veterinary officer Christine Middlemiss said: “I have declared a national Avian Influenza Prevention Zone (AIPZ) legislating for actions all bird keepers must take to help prevent the disease spreading to more poultry and other domestic birds.
“Public Health England has confirmed that the risk to public health is very low and the Food Standards Agency advises that bird flu poses a very low food safety risk for UK consumers.
“Whether you keep just a few birds or thousands, you are now legally required to meet enhanced biosecurity requirements and this is in your interests to do, to protect your birds from this highly infectious disease.”
Cases are rising across Europe as Poland, Croatia and Slovenia recorded their first incidents of H5N8 last week, caused by a strain which was first detected in Iraq in May, according to Poultry Network.