Her article appeared ahead of a major parliamentary conference on misogyny and antisemitism, which will discuss research showing Jewish women MPs receive 15 percent more mentions on a far-right website than their male counterparts.
Ms Smeeth wrote that these attacks were "turning away" Jewish women from public life.
She said women such as the Holocaust Educational Trust's Karen Pollock and actress Tracy-Ann Oberman were receiving "misogynist and racist abuse for having the audacity to participate in our national conversation is hardly an incentive for young Jewish women to get involved".
"Anyone that knows me will know that I refuse to be cowed, bullied, intimidated or threatened. Antisemites in my own party have failed to force me to leave. Misogynists and racists online will not grind me down or push me out," she wrote.
"I’m proud to be a British, Jewish woman in public life and I’m not going anywhere."
