Officials insisted there was "no nuclear risk" from the blaze, which broke out at BAE Systems' site at Barrow-in-Furness in Cumbria in the early hours.
The Royal Navy's nuclear-armed and nuclear-powered submarines are built at the shipyard.
"Emergency services remain in attendance at BAE at a significant fire at the site," the Cumbria Local Resilience Forum said in a statement released by police.
"There is no nuclear risk," it added.
An earlier statement noted that the two people had been taken to hospital for suspected smoke inhalation.
People living near the shipyard were told to keep doors with windows closed and avoid the area while emergency services remain there.
"Cumbria Fire and Rescue are likely to have appliances on site for much of the day today," the statement added.
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