In a tweet, Parker, who is Environment, Ocean and Fisheries and Revenue Minister, as well as the Attorney-General, said he was isolating at home after testing positive on Sunday, had minor symptoms and was "not feeling too bad".
The 62 year old had not been in the Beehive since last Monday, so was not with other MPs or staff while infectious, he said.
His tweet on Monday afternoon read: "Just thought I’d let people know I tested positive for Covid on Sunday. Isolating at home. Some minor symptoms but not feeling too bad. Haven’t been in the Beehive since Monday, so fortunately not with other MPs or staff while infectious."