Currently on bail, he has been charged with making a false declaration on a travel document.
The case is considered historical, presenting a low risk to the public.
Health Secretary Bob Williams says the man arrived in Auckland from Egypt on 5 May, where he tested positive for the virus in managed isolation.
He tested negative before being released from quarantine after which he flew to the Cooks, where he tested positive on 5 June.
All his close contacts have tested negative.