The actress, who plays Sunita Alahan in the ITV1 soap, could contact police after she was taunted about her Indian heritage on the website, the Sunday Mirror reports.
A friend said: "Shobna's a strong woman but this really shook her up. She put on a bit of a front in her Twitter posts because she didn't want to give this person the satisfaction of seeing her get upset."
Gulati addressed the abuse on Twitter, saying: "Surprised at the racial abuse and desire to hurt people for no reason. Might give Twitter a wee rest... weirded out!"
She previously admitted that she hates it when fans tell her how she looks on television.
Gulati recently embarked on a charity trip to Africa with several other celebrities.