Among the fans sending Perkins messages of support was TV presenter Fearne Cotton who tweeted: "There are some awful and sad humans out there. How pathetic. ps you absolutely rock!"
Her co-star Paul Hollywood wrote: "There are some strange people out there but nicer people too be with you soon Sis xx."
The corporation investigated the ousted Top Gear presenter after he attacked one of the show's producers, splitting his lip and abusing him in a 30-second verbal assault on March 4.
He was initially suspended by the broadcaster on March 10 for the attack on Oisin Tymon, before it announced his contract would not be renewed.
Clarkson will appear on stage with his former Top Gear colleagues Richard Hammond and James May later this year to fulfill a series of shows planned before he left the BBC.
They will be stripped of all BBC branding and instead be presented as Clarkson, Hammond and May Live.
That means the show which will tour Australia, Norway, South Africa and the UK will not be able to use clips from the show - or even feature the Stig.
Sue Perkins is not the only celebrity to have left Twitter due to bullying and trolling.
Downton Abbey star Lily James quit after trolling from fans who did not like her Downton storyline.
In 2012, Little Britain star Matt Lucas left Twitter for some time after a 16-year-old tweeted him a joke relating to his former partner's death.
Lucas replied saying: "I'm not joking. I think you should delete that tweet. It really upset me."
- Daily Mail