The Avengers actor was photographed wearing a navy uniform on HMS Prince of Wales on Thursday and Friday (May 12 and 13).
Movie news websites claim the production is for the directorial debut of English actor Kristen Scott Thomas, which will also feature Sienna Miller – although she was not pictured on location.
They said Johansson could be seen making a speech to members of the navy.
It is thought the film will tell the story of the first female naval commander.
This comes as The News reported how several production vans had set up camp in a car park at the Lakeside North Harbour site in Cosham last week where they were due to remain until May 14.
The convoy was acting as a hub for filming on location at Portsmouth Naval Base further south in Portsea.
Although crew members were unable to disclose exactly what they were working on, several readers came forward to say Johansson had been seen at HM Naval Base.
Other readers also said they saw her Avengers co-star Chris Evans at the base, believing the pair were shooting for a new Apple TV feature called Project Artemis, however, it is thought this is actually a separate project.
In response to a query by The News last week, a Royal Navy spokeswoman said: ‘For commercial reasons it would be inappropriate to comment.’