The incident is reported to have taken place aboard the Liberian-registered Nave Andromeda crude oil tanker south of Sandown, according to Isle of Wight Radio.
A Hampshire police spokesman said: “We are aware and dealing with an ongoing incident on board a vessel which is situated south of the Isle of Wight.
“We will provide you with further updates when we are in a position to do so.”
It is understood that the 228-metre tanker had been expected to dock in Southampton at 10.30am on Sunday.
A spokeswoman for Associated British Ports (ABP) said it had no comment on the incident.
It is understood the port received contact from the ship but it had not been refused entry to the harbour.
Two coastguard helicopters have been scrambled to the scene and were spotted circling the ship on Sunday afternoon, and an exclusion zone was set up in the area south of Sandown.
A Coastguard spokeswoman said: “We are currently assisting Hampshire Constabulary with an incident on board a vessel situated off the Isle of Wight.
“The search and rescue helicopters from Lee on Solent and Lydd are in attendance.”
A spokeswoman for the UK Home Office said it was aware of the incident.
