Ruth Burke, 82, passed away last night in Antrim Area Hospital and her family has asked for her to be named.
They said she was simply unable to fight the disease.
As Coronavirus is so contagious, those who die with it must be placed in closed coffins.
Mrs Burke’s daughter Brenda said the family did not want her simply to be remembered as a statistic.
She said it was heartbreaking not to be able to see her in her coffin and kiss her goodbye.
Brenda Doherty told BBC Radio Ulster’s Talkback her mother was a “strong woman” and a “loving mother”.
She said: “She lived for her grandchildren and great-grandchildren – they put smiles on her face.
“There is a frustration that people don’t understand, they’re not being respectful of what they’re told.”
In a video posted on her Facebook page, Ms Doherty said her mother had an “unbelievable strength and suffered many challenges in her life”.
“Unfortunately this was one she was not going to overcome,” she added.
On Monday 20 new cases of coronavirus were confirmed in the North of Ireland, bringing the total to 148.
figures for Tuesday have yet to be released by Department of Health officials.