Britain's Royal Navy and Royal Air Force routinely shadow potential threats to national security, and such missions to monitor Russian vessels and submarines have become more frequent since Russia invaded Ukraine in 2022.
Healey said directing lasers at RAF pilots was "deeply dangerous" and Britain was poised to react depending on the Yantar's next move.
"We have military options ready should the Yantar change course," Healey said.
"My message to Russia and to (Russian President Vladimir) Putin is this: we see you. We know what you're doing. And if the Yantar travels south this week, we are ready," he added.
Responding to what it described as "endless accusations", the Russian embassy in London said: "Our country's actions do not affect the interests of the United Kingdom and are not aimed at undermining its security.
"We are not interested in British underwater communications," it said, urging "the British side to refrain from destructive steps that exacerbate the crisis phenomena on the European continent."
The Yantar, designed for intelligence gathering and mapping undersea cables, is currently on the edge of British waters, north of Scotland, Healey said.
He added: "This is the first time we've had this action from Yantar directed against the British RAF. We take it extremely seriously."
"I have changed the navy's rules of engagement so that we can follow more closely, monitor more closely, the activities of the Yantar when it's in our wider waters."
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