"At approximately midday Dubai time on March 28, the Crude Oil Tanker the MV ZIRKU was pirated approximately 250 nautical miles southeast of Salalah in the eastern part of the Gulf of Aden," EU Navfor said on its website.
It was not immediately clear whether the tanker was fully laden with crude. Sudan is an oil-exporting country.
But Kuwait's state oil company denied the report as "totally incorrect", state news agency KUNA reported.
"Kuwait Petroleum Corporation has denied reports saying that a Kuwaiti oil tanker was seized off Oman's coast," KUNA reported.
KPC spokesman Sheikh Talal al-Ahmad al-Sabah, quoted in a brief statement, said the report from the European Union Navfor anti-piracy mission was "totally incorrect."
Tankers are a prized catch for ransom-seeking Somali pirates who operate as far south as Madagascar and as far east as a few hundred miles off India.
Somali pirates early last month grabbed a US-bound super tanker carrying a crude oil cargo worth an estimated $200m.
Somalia has lacked an effective central government for two decades, allowing armed gangs to stalk the strategic waterways off the Horn of Africa nation and rake in tens of millions of dollars in booty each year.
EU Navfor said the tanker's 29-strong crew included one Croatian, 17 Pakistani nationals, one Iraqi, one Filipino, one Indian, three Jordanians, three Egyptians and two Ukranians.