The hole appeared on the road just outside the National Historic Landmark in Palm Beach, where the Trump Organisation operates a private club.
The Palm Beach Post reported that the 1m radius hole appeared on Monday to the west of one the resort’s entrances.
It is near a new water main and isn’t a threat to the President’s property, Palm Beach County authorities said.
Among the guests who have stayed are Japan’s Prime Minister Shinzo Abe and Chinese President Xi Jinping.
The resort has now closed for the summer.
Mr Trump bought the estate in 1985 for $10m and embarked on a multimillion dollar improvement programme.
Each of the club’s 500 members pays $14,000 annually in dues after paying an initiation fee, which currently stands at $200,000.