The Downton Abbey actress was admitted on Friday (November 2) after complaining of severe pains, according to the Sunday Mirror.
The 77-year-old, who stars as Violet Crawley in the ITV1 drama, was taken to a cardiac unit at the Wellington Hospital, London and reportedly underwent a series of tests before being discharged later that day.
A source told the newspaper that "it was a big scare" for Smith, adding: "It was extremely distressing for her but she did the right thing and made sure she got to hospital as soon as possible."
The insider went on to question Smith's future in Downton Abbey, saying that she would "have to think very carefully now about whether she stays in the show".
"Her health always comes first and I am sure she will take advice from the experts," they added.
Smith has previously suffered from breast cancer, and in 2009 revealed that she thought about ending her career after going through chemotherapy and radiotherapy.