The spokesman said: "This was an irresponsible act because she could have put the safety of MoD police at risk if she had got into trouble in the water.
The security breach at the Faslane Naval Base on the River Clyde occurred at 0548 BST on Friday.
It is believed the female protester managed to avoid detection by swimming for several hours to get inside the high security berth.
An MoD spokesman said the woman has been charged in connection with the incident and a report has been submitted to the Procurator Fiscal.
The spokesman said: "This was an irresponsible act because she could have put the safety of MoD police at risk if she had got into trouble in the water.
"We do have good security at the base, but no security is impenetrable. There will be a thorough investigation."
The investigation will centre on how the woman managed to penetrate the security cordon which surrounds the home of Britain's nuclear submarine fleet.
After swimming for several hours she approached one of the berthed nuclear submarines and spray painted the side of the hull.
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The woman was arrested within seconds of emerging from the water.
This is the second time in a month that female anti-nuclear protesters have breached security.
In March, seven women were arrested after chaining themselves to a French Navy Frigate which was docked near the Faslane.
They managed to cut through a wire security fence before unfurling a banner which read: "Women of the world unite for a world without war".
In February politicians and church ministers were among 379 people arrested following a similar protest outside the naval base.