Shadow chancellor John McDonnell said that “discussion” would happen in the party because of what he said was a “change in coverage” on the channel since the poisoning.
He spoke out after viewing coverage on the network, which is accused of being a mouthpiece for Vladimir Putin, which he said had “gone beyond that line” of objective journalism.
Russia has been accused of being behind the nerve agent attack in Salisbury on Mr Skripal and his daughter Yulia – both of whom are still fighting for their life in hospital.
However, no one has been arrested in connection with the crime.
Mr McDonnell said he would not appear on RT – formerly known as Russia Today – and added that the party would discuss whether other members should follow suit.
“I think that is right now and that is what I will be doing,” he told the BBC’s Andrew Marr Show. “What we are seeing from Russia Today sometimes goes beyond objective journalism from what I’ve seen.
“I have been looking overnight at some of what’s happening in terms of the change in coverage on Russian television in particular and I think we have to step back now.
“I can understand why people have (appeared on RT) up until now because we have treated it like every other television station.
“We tried to be fair with them and as long as they abide by journalistic standards that are objective that’s fine but it looks as if they have gone beyond that line, so yes, we will have that discussion.”
The Independent has contacted RT for comment, but none had arrived at the time of publication.
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Critics of accuse the network of being a mouthpiece of Vladimir Putin’s government and say it broadcasts English language propaganda to improve Russia’s image abroad.
Supporters of the network argue that the channel’s coverage of the country is fair and that it serves as a tool to counteract the mostly anti-Kremlin bias served up by the media in the West.
Ofcom in December launched an investigation into Alex Salmond‘s TV show on the station over claims it had breached its “rules on accuracy”. It has yet to make a ruling.