Both Mr Interian and and Ms Gonzalez allegedly failed to follow an isolation order from the Florida Department of Health in Monroe County requiring the couple to remain at home for 14 days and wear face masks around others, according to the newspaper.
A property manager at their apartment complex was said to have told authorities the couple was not complying with the quarantine and going about their daily lives as usual.
A police report alleged Mr Interia had made several trips outside his home without wearing a mask including to walk his dog, go to the grocery store, and wash his car.
Both were charged with violating the state law requiring isolation or quarantine in a public health emergency and violating emergency management, The Herald reported.
Both charges could be punishable by up to 60 days in jail.
Mr Interian and and Ms Gonzalez were both reportedly released from the Stock Island Detention Centre on Thursday after posting $1,000 (£764) in bail each.
The state of Florida has 461,000 confirmed cases of the virus and more than 6,500 deaths as of Friday.