The pups perished at St Abb's Head national nature reserve in Berwickshire, in a bay at Pettico Wick.
Rangers there found 224 dead grey seal pups in the water, with "many more" washing up on the shoreline.
Workers at the site, which is run by the National Trust for Scotland (NTS) conservation charity, say the extent of damage from the storm was unprecedented.
The St Abb’s reserve has seen a massive increase in seal pup numbers over the past decade.
Surveys in 2007 showed there was no colony at the site but a record number of more than 1,800 pups were counted there in 2020.
NTS ranger Ciaran Hatsell, who is based at the reserve, posted the bad news on social media.
“While the first concern is always human life, we then begin to worry about the effects of the storm on our wildlife,” he wrote.
“Having worked on seal colonies for 10 years I’ve never seen a storm cause damage on anything like this scale before.
“Unfortunately it appears we have lost the majority of our seal pups to this storm.
“In a small area of bay at Pettico Wick there were 224 dead pups in the water, with many more washing up ashore.
“We are planning to do another survey this week to see what the damage is to the rest of the colonies but it doesn’t look good.
“This is a risk grey seals take with their breeding strategy, pupping at this time of year when storms are most frequent.
“But for this kind of phenomenal storm to hit at the peak of pupping is exceptional.”
He said several trees had been torn down during the high winds and electricity at the reserve was cut off.
Stuart Maxwell, NTS general manager for Edinburgh and East, said: “The damage caused by Storm Arwen is as shocking as it was unexpected.
“Thankfully no-one has been hurt but the lingering effects of the storm mean that the local community has been without power and this has been hampering our efforts to ensure the reserve is made safe.
“We’re expecting to have to use a lot of our charitable resources in clearing up fallen trees and other debris.
“As our ranger Ciaran noted in his social media post, the loss of seal pups to this brutal storm was substantial and certainly the worst that any of us have ever seen.
“We can’t be certain of the full extent of the loss until we’re in a position to conduct a survey later on in the week.”
He said many NTS places up and down the east coast were badly affected by the extreme weather over the weekend, with damage to trees and buildings and loss of power.
As a result, many properties are currently closed to the public while NTS teams focus on making places safe and clearing up the devastation.
He urged people to check before travelling to any sites for the next few days.