Footage shows Farrukh, 38, using the inflammatory word during a political rally outside the Council House in Birmingham last month.
In a video, Farrukh, a businesswoman and journalist, is seen standing on the steps of Birmingham's landmark Victoria Square and telling supporters: "There is only one slogan for today. It is remove curfew from Kashmir. Let them live their own lives nothing more than that.
"And one thing to truth-tell to the Muslim community! There's only one solution which is jihad. No protest, nothing. Just jihad."
A resident of Bordesley Green, Farrukh has described herself in the past as a "social worker", "philanthropist" and "chief executive" of a Muslim TV channel, Noor TV.
The police have visited Farrukh at her home in Birmingham and have confirmed that an investigation is going on.
On her part, Farrukh denied inciting violence, insisting that she was referring to "a struggle".
When quizzed about her speech, Farrukh said: "'Jihad' doesn't have one particular meaning. If you have a problem with the Government of the UK and you want to raise your voice, the struggle is called 'jihad' in the meaning of Islam. Do you think I'm the kind of person who would use that word to encourage people to go and fight?"
West Midlands Mayor Andy Street said: "The comments made by Sumaira Farrukh go completely against the spirit of the Faith Conference and its steering group, which promoted tolerance and respect."
( With inputs from IANS )