The Prime Minister's Withdrawal Agreement was defeated in the vote.
Thousands of protestors had gathered outside the building on the day Britain was due to leave the European Union.
Ms Nandy described the atmosphere as 'not normal' and said staff had been advised to leave the building for their own safety.
She tweeted yesterday morning: "Today outside Parliament I and others were accosted by people shouting f****** traitor as we tried to get in to vote. Our staff were advised to leave the building for their own safety. There were armed police everywhere. This is not normal."
SNP MP Joanna Cherry also tweeted, describing the atmosphere as "very intimidatory".
She added: "Very relieved to be safely back to my base in London. Was abused by trailing ends of the #LeaveMeansLeave protest as I walked home. Called a traitor. Told to go back to my own country. Such a contrast from #PeoplesVoteMarch last weekend #BrexitChaos."
Five people were arrested by the Metropolitan Police outside Parliament during the protest yesterday.
It included one man on suspicion of assaulting a police officer and another who wanted for an offence in Hertfordshire. Two people were arrested for assault and one for being drunk and disorderly.
Some protesters were seen jostling with journalists and police. Some were caught on film appearing to push camera crews away from a crowd of people.