The White House cited "grave national security risks and privacy concerns" as the reason for its decision.
Former President Barack Obama voluntarily disclosed more than 6 million records during his presidency.
Critics say the logs allow for monitoring of individuals or groups who may be trying to influence policy.
White House Communications Director Michael Dubke said the administration is following a 2013 federal court ruling that found most of the logs are considered presidential records and are not subject to the Freedom of Information Act (FOIA).
He argued Mr Trump has taken steps to improve ethics such as imposing new restrictions on lobbying and opening to the White House news briefing room to outlets that previously did not have access.
Senior White House officials also contend Mr Trump's new policy mirrors what previous administrations have done before Mr Obama.
The Obama administration began releasing visitor records in September 2009 in response to legal challenges.
The policy had some exceptions, which included private visits to the Obama family and those in attendance for "sensitive meetings", such as potential Supreme Court nominees.
But the records were not made available immediately and sometimes took months before they appeared online.
White House lawyers also redacted names for national security concerns and other reasons before the logs were made public.
In 2012, Mr Trump criticised Mr Obama for concealing names.
Under the new directive, records of those entering the White House complex will be kept confidential until at least five years after Mr Trump leaves office.
But White House agencies such as the Office of Management and Budget and the US Trade Representative may be subject to Freedom Of Information Requests.
Earlier this week, a coalition of watchdog groups filed a lawsuit against the Trump administration with the aim of publishing the visitor records.
The Obama administration published the logs on a White House-maintained web page. Since Mr Trump took office, the page has been shuttered.
White House officials said on Friday they would no longer maintain the web page and said it would save taxpayers $70,000 (£55,867) by 2020.
Democratic lawmakers have also proposed legislation that would require the Trump administration to disclose the names of visitors at other places where he conducts business, including his Mar-a-Lago estate in Florida.
Mr Trump has been widely criticised for his lack of transparency. He has repeatedly refused to release his tax returns, breaking with decades of precedent.
Thousands of protesters are expected to march on Saturday in cities across the US calling on Mr Trump to release his personal tax returns.