One of the affected people has been admitted to the Reina Sofía Hospital, where a tent has been installed outside to carry out the tests.
The health authority says all the other guests at the wedding, together with close contacts, also have to self-quarantine for 14 days.
All those tested positive are over the age of 50.
It is believed that the virus was imported from another part of Spain by a guest who had travelled for the wedding.
The mayor of Tudela, Alejandro Toquero has made a plea for “collective and individual responsibility” and says he is in close contact with the health authority to monitor developments.
An investigation is already underway to try and find the source of the new outbreak.
The mayor has warned that if there are further outbreaks, restrictions could be reimposed by the Government of Navarra and Tudela city council.
This could be bad news for tourists visiting the area, which is famed for its history and famous architecture.
“Once again, responsibility is requested and an appeal is made to continue with the measures of social distancing and a mask,” Mr Toquero said.
Navarra’s health chief, Santos Induráin said the number of people affected at the wedding was almost certain to increase and tests would be taken both now and at the end of seven days initially and then at 14 days.
Confirming the cases were being treated as outbreaks, she warned: “The virus is still here and people must be vigilant.”
“The Department of Health, in contact with both the local and health authorities in these areas, is currently working to complete the monitoring of the two new outbreaks and to adopt the necessary measures to tackle the possible chain of infections,” she said.
Additional reporting by Rita Sobot