The elections watchdog has warned that it may be an offence to share information obtained at postal vote opening sessions after Ms Kuenssberg that while parties are not supposed to look at voting papers when they are verified - but not counted - at opening sessions, they do "get a hint" of how they are doing and that it painted 'a grim picture' for one of the main parties.
A video of her remarks, made during an interview on the BBC's Politics Live programme, was widely shared on social media and appeared to provoke a response from the Electoral Commission.
In a statement on Twitter, the watchdog said: "It may be an offence to communicate any information obtained at postal vote opening sessions, including about votes cast, before a poll has closed.
"Anyone with information to suggest this has happened should report it immediately to the police."
Ms Kuenssberg made the comments after being asked about voter turnout in Thursday's election during a live interview with the BBC Two show on Wednesday.
She said: "The forecast is that it's going to be wet and cold tomorrow, the postal votes, of course, have already arrived.
"The parties - they're not meant to look at it, but they do kind of get a hint - and on both sides people are telling me that the postal votes that are in are looking pretty grim for Labour in a lot of parts of the country.
"Of course postal voters tend to skew to elderly voters and people who vote early... but the kind of younger generation who we know skew much more to the Labour Party you might expect to turn out to the polls tomorrow.
"But in this winter election, turnout is just another one of these factors that we just can't predict."
The comments immediately led to people tweeting the Commission to complain, with many also stating they intended to take the matter up with the police.
One person wrote: "There is a BBC reporter called Laura Kuenssberg who is making statements about how people have voted, in advance of the count. What are you doing about it?"
While another called for her to be sacked, adding: "This represents a breach that could damage the outcome of the election. How does she know this? What motivates this disclosure? She has disgraced journalism and the matter must be addressed at the highest level."
A BBC spokeswoman said: "The BBC does not believe it, or its political editor, has breached electoral law."
Party candidates and agents can observe postal votes being verified, but the ballot papers are placed face down and not counted until polls close on election day.