Mr Grant apologised for a tweet, which said: “Jacob is a Catholic Brexiteer. On Fridays he only sells out fishermen.”
The tweet, which the Glenrothes MP later deleted, referred to the EU transition deal that has seen leaving the common fisheries policy delayed for a year as well as the Catholic tradition of eating fish on a Friday.
Mr Grant, who is also a Catholic, said sorry in another tweet.
He said: “I’ve deleted a tweet I sent out about Jacob Rees-Mogg. I intended no offence to anyone who shares my faith but I now accept that it was ill-judged and I apologise for any offence caused.”
Ross Thomson, the Tory MP for Aberdeen South, said targeting someone because of their faith was “not acceptable”.