The incident occurred late Saturday or early Sunday local time. At least one missile was fired, the officials said.
"The Mason once again appears to have come under attack in the Red Sea, again from coastal defense cruise missiles fired from the coast of Yemen," Navy Admiral John Richardson, chief of naval operations, told reporters at an event in Baltimore Saturday.
The destroyer was targeted by missiles fired from rebel-controlled areas in Yemen twice earlier this week, prompting the U.S. military to launch cruise missiles that destroyed three radar sites in response.
After the earlier attempted missile attacks this week, a Defense Department official warned that those who fire on U.S. vessels do so at their peril.