McCullum, 31, took over from Ross Taylor in controversial circumstances in December, prompting criticism of both the new captain and national coach Mike Hesson from sections of the New Zealand cricketing community.
A nine-page report leaked to media this month made accusations about how McCullumcame to win the top job.
In a statement issued through his lawyers, McCullum said he believed Parker, a 62-year-old former Test batsman, wrote the document and he will file proceedings in court next week seeking a retraction of the claims.
"Mr Parker's paper makes some very serious attacks on my integrity, my honesty and my ethics as a professional sportsman," he said. "I have endeavoured to resolve these issues with Mr. Parker but have been unable to do so.
"He has left me with no choice but to defend myself and my reputation this way."
McCullum, who is currently playing in the Indian Premier League, said he was paying for the legal action himself and would not pursue monetary damages, simply a retraction from Parker.
Hesson said in a statement that he had voiced similar concerns to McCullum about statements made by Parker, adding: "I have taken legal advice and the matter is currently being dealt with by my lawyers."