The EastEnders actress - who plays Denise Fox in the soap - explained that she was about to pick her children up from school at her home in Bush Hill Park when she found the tree on top of her car.
The tree had also brushed the outside of her home and sent debris around the property.
Parish explained that neighbours in the area had been complaining about the trees for a while due to their age, after other trees had fallen down in previous years.
"It could have killed my family. I was five minutes away from picking the kids up from school, who knows what could have happened?" she told the Enfield Independent.
"There have been so many complaints from people on this road to the council about this, it's ridiculous.
"It's ruined my car but thankfully everyone is fine, but I'm so angry about it."
Diane Parish has played Denise Fox in the BBC One soap since arriving in 2006. She recently praised Pam St Clement's final "moving" scenes in the soap as Pat Butcher.