The tweet on Monday said the military was ready if ever needed to drop "something much, much bigger" than the New Year's Eve ball in New York City, whose descent at Times Square marks the arrival of the New Year, Xinhua news agency reported.
It also showed a video of an aircraft releasing bombs and explosions on the ground.
The message was deleted later from the Strategic Command's twitter feed, while a new message said the previous one was "in poor taste".
"We apologise," the subsequent tweet said. "We are dedicated to the security of America and allies."
Twitter users responded to the message with confusion and unease.