Defence Secretary Ben Wallace warned "the lights could go out" if national infrastructure was lost, and the cables were "incredibly important".
He also told the BBC's Andrew Marr that Russia had "taken a deep interest" in the cables and the UK would be "deeply exposed" without further measures.
It comes ahead of Monday's publication of the defence command paper.
The document will give more detail for the armed forces on the conclusions of the integrated review of the UK's foreign and defence policies.
But some parts were already announced this week, including the lifting of the cap on the number of nuclear warheads the UK holds in its stockpile.
The government had previously committed to reducing the level to a maximum of 180 by the middle of the 2020s, but the move would allow the number to reach 260.
Mr Wallace said it would ensure the country's nuclear deterrent was "credible", and would still be lower than other nations - pointing to France, which has 300.
But Labour's shadow foreign secretary Lisa Nandy said the proposal had "baffled" opposition parties and they would not support it until the measure had been justified by the government.
Hundreds of thousands of miles of undersea cables circle the globe, providing internet and communications links between nations and continents.
The Ministry of Defence said they are "vital to the global economy and communications between governments" and are at "risk of sabotage" due to "submarine warfare".
The new Multi Role Ocean Surveillance ship will be fitted "with advanced sensors and will carry a number of remotely operated and autonomous undersea drones which will collect data".
The vessel, staffed by 15 people and due to come into service in 2024, will carry out operations in both UK and international waters.
The MoD added it will also "be able to support with other defence tasks, including exercises and operations in the Arctic which will become an increasingly contested area".
Undersea cables carry more than 90% of the world's communications - including trillions of dollars worth of financial transactions every day.
There's growing concern these underwater arteries could be vulnerable to attack.
British and US military and intelligence officers have recently warned of Russian submarines "aggressively operating" near Atlantic undersea cables.
The Ministry of Defence says there's a risk of sabotage - which presents an existential threat to the UK.
As part of a wider defence review - the MoD will order a new Royal Navy surveillance ship to monitor this critical infrastructure.
Mr Wallace told the BBC: "The lights could go out if we lose our critical national infrastructure across the board. Cables are one part of that critical national infrastructure and incredibly important.
"Russia has certainly taken a deep interest in those cables, not only to the United Kingdom but obviously to the continent of Europe.
"[The vessel's] job is going to be to protect not only critical national infrastructure, but other things. It will be able to do other surveillance functions around the sea and everything else and I think it is really important that we invest in t hat because otherwise we are deeply exposed."
Prime Minister Boris Johnson has promised his plan for modernising the armed forces and foreign policy will help make the UK "match-fit".
The Integrated Review, first announced in 2019, will set out the UK's defence and foreign affairs priorities for the next decade or so, during which cyber warfare in particular is expected to become a greater threat.
Broader foreign policy from the review was announced this week, with Foreign Secretary Dominic Raab pledging to boost alliances in the Indo-Pacific region, describing it as "increasingly the geopolitical centre of the world".
But more on how the Armed Forces could be overhauled will be announced on Monday, following a boost in funding late last year.
The defence secretary was pushed by Andrew Marr on what the new command paper would mean for the size of the forces, but Mr Wallace said that was a decision for Parliament.
He added: "What I can give you is the assurance that we have had a record settlement, so I am making decisions, not in an environment of falling tide like in previous cuts, but in an environment where I am going to make the decision to have the right Armed Forces to match our ambition and meet the threat."