Louise Haigh, MP for Sheffield Heeley, wrote an open letter to the incoming Rt Rev Philip North about what she calls his "troubling" views.
Bishop Philip has historically held a traditional view on women in church leadership - a position which has caused him difficulty within the Church of England, which allows women to become vicars and bishops and also ordain men.
The current Bishop of Burnley previously turned down an appointment to become the Bishop of Whitby in 2012 because of friction over the issue.
There were calls for him to turn down his nomination to become Bishop of Sheffield after his appointment was announced in January, but since then 36 female Church of England clergy including bishops signed a letter affirming their support of Rt Rev Philip's selection, affirming his qualities as a church leader and the need for a diverse range of opinions to be represented in the Church.
Louise Haigh said in her letter: "Your traditionalist views pose many questions about how your leadership in Sheffield will work practically in relation to existing women clergy, men who have been ordained by women, women who are in the process of becoming clergy and congregations who come from a completely different tradition within the church.
"... I would urge you to engage with congregations and individuals within the church to answer questions that are troubling people in Sheffield and to establish if your views can possibly be reconciled with the pastoral and public image of the church in Sheffield.
"I look forward to discussing these concerns with you face-to-face soon."
Rt Rev Philip North is due to be installed in June and has previously said he is "determined to be a bishop for all and develop the ministry of all clergy - male and female."
