Police requested military assistance and a 4.8km exclusion zone had been placed around the vessel, the Nave Andromeda, currently near the Isle of Wight off the south coast of England, on Sunday.
"Isle of Wight Radio understands that seven suspects have been detained onboard the Nave Andromeda," the station reported. "Special forces from Poole have been involved."
The Special Boat Service, a naval special forces unit that works closely with the Special Air Service (SAS), is based in Poole in southern England.
A spokesman for the Defence Ministry declined to comment on the report.
It was not immediately clear where the suspected stowaways were from or what their intentions were.
Thousands of illegal economic migrants and would-be asylum seekers have sought to cross the English Channel from France to reach British shores this year, often paying people traffickers to help them traverse one of the world's busiest shipping lanes in overloaded rubber dinghies.
Police said the crew had been subject to threats from stowaways and that they were working with coastguard and border forces to resolve the situation.
"It was reported that a number of stowaways were on board, and they had made verbal threats towards the crew. No one has been reported injured," a police spokesman said.
The coastguard agency said search and rescue helicopters were attending but did not give details.
Refinitiv vessel tracking data showed the Liberia-flagged Nave Andromeda had been expected to arrive in the English port of Southampton at 10:30 GMT on Sunday. The vessel had left from Lagos, Nigeria, the data showed.
The Nave Andromeda's registered owner is Folegandros Shipping Corp, and the vessel is managed by Greek shipping company Navios Tankers Management Inc., according to Refinitiv.
In December 2018, British forces stormed an Italian cargo ship and regained control after stowaways threatened crew as it sailed close to the southeast coast.
