Ms Smith, who is fully vaccinated, said on social media that she had contracted Covid-19 over Christmas.
And she said she was "wiped out" by the "nasty" virus, which had left her feeling too tired to walk upstairs.
"Please get vaccinated and take up the booster. I’m young(ish), I eat healthy, I exercise and Covid has wiped me out," Ms Smith said on Facebook.
"Without vaccinations I dread to think how sick I would be right now, so please take up a vaccine even if you feel superhuman because this virus is nasty."
On her Twitter account, the MP joked: "My brother-in-law gave me Covid for Christmas, last time I complain about getting socks.
"I’m managing at home but I’ve not got dressed in days & I can’t walk up stairs without having a nap. I dread to think how sick I might have been without 2 jabs & booster #GetVaccinated"