Cross was contacted by PRWeek but declined to comment on the development, adding that it was an "extremely private matter".
It is not yet clear why Cross was suspended or for how long.
However, in a statement agreed by Cross and John Lewis, the company said: "Peter Cross is unavoidably away from the business for personal reasons. We are expecting him to return shortly."
Cross was appointed by the retailer in January 2013 and took up his post six months later. He was previously managing director of PR agency Portas, formerly known as Yellowdoor.
He succeeded Helen Dickinson, who had been John Lewis' director of communications since 2000.
Commenting at the time of Cross' appointment, John Lewis' managing director Andy Street said Cross had inherited a highly effective comms team developed under Dickinson’s leadership and that he brought with him a "broad understanding of the UK consumer and the revolution under way on the British high street".