"Our naval forces fired corresponding ship-based missiles at a US destroyer USS Gravely in the Red Sea," Houthi military spokesman Yahya Saree told during a televised address.
All US and UK ships in the Red and Arabian seas that were involved in attacks against are considered as potential targets of Houthi strikes, he said.
Earlier, US Central Command (CENTCOM) said in a statement that a US Navy warship had shot down a Houthi anti-ship missile fired from Yemen toward the Red Sea.
"On Jan. 30, at approximately 11:30 p.m. (Sanaa time), Iranian-backed Houthi militants fired one anti-ship cruise missile from Houthi-controlled areas of Yemen toward the Red Sea. The missile was shot down by USS Gravely (DDG 107)," CENTCOM said on Tuesday.
There were no injuries or damage reported in this incident, according to CENTCOM.
Iran has repeatedly rejected accusations from Western countries over Tehran's alleged involvement in the Houthi attacks on merchant ships in the Red Sea. In addition, Iran emphasized that resistance groups in the Middle East, such as the Houthis, do not receive any instructions from Iran.