Thompson won a gold, silver and bronze medal at the 2012 Summer Paralympics, and a silver and bronze at the 2016 Summer Paralympics as a "pilot" for blind cyclists Phillipa Gray and Emma Foy.
She won eight gold medals between 2014-16 and was appointed a Member of the New Zealand Order of Merit for services to cycling in 2013.
Thompson told Newshub she first felt ill five days ago, before testing positive for Covid-19 on Monday.
She urged New Zealanders to take the virus seriously and to care for their families, their communities and the most vulnerable.
"If your loved ones are sick they lie in hospital alone, you can't visit them, you can't do anything."
Her young children haven't been able to go to the park or see other family members for fear of spreading the virus and she wasn't even able to hug them, Thompson said.
"People cannot become complacent," she told Newshub.
"I was told I was over the top with the precautions I took leading into the lockdown."
Checkpoints will be set up across the country at holiday hotspots and anyone thinking of sneaking off for the long weekend should rethink this immediately, he said.