The privately held New York company said it made its decision after speaking with White House lawyers last week.
The ad, which shows the president during a visit to the Great Wall of China, went up without Obama's permission, clashing with a White House policy disallowing use of the president's image or likeness for commercial purposes.
"We made the commitment to the White House, and we are going to take it down even though it's a very gray area and we were advised by a lot of people to leave it up," company President Freddie Stollmack told Reuters.
"In this case, discretion is the better part of valor," he said. "We don't want to alienate the White House and win the battle and lose the war."
The ad won't come down immediately. Stollmack said a new advertisement had to be created first.
(Reporting by Daniel Trotta; Editing by Ellen Wulfhorst and Cynthia Osterman)