In a post on Friday, the site said it had suspended 61 accounts that were part of a co-ordinated effort, the BBC reported.
The documents had their first wide burst of public attention when unveiled in the election campaign by opposition Labour Party leader Jeremy Corbyn.
Corbyn claimed the documents revealed that the National Health Services (NHS) were up "for sale", adding that their release was in the public interest.
The Conservative government said it was "looking into the matter", but declined to comment on the development.
The original Reddit post containing the trade talks documents came from an account with the user name "gregoratior".
But the post did not provide any further details about the evidence behind its conclusions.
It however, said that a group of suspect accounts "provides us with important attribution for the recent posting of the leaked UK documents, as well as insights into how adversaries are adapting their tactics".
"We investigated this account and the accounts connected to it, and today we believe this was part of a campaign that has been reported as originating from Russia.
"Suspect accounts on Reddit were recently reported to us, along with indicators from law enforcement, and we were able to confirm that they did indeed show a pattern of coordination," the post continued.
Meanwhile, the Labour Party has not commented on how they obtained or became aware of the documents.
A party spokesperson said: "These documents reveal the plot against our NHS. And of course neither the UK nor the US government have denied their authenticity. Our releasing them to journalists was clearly in the public interest."
( With inputs from IANS )