Alun Cairns, the Vale of Glamorgan MP, was reappointed as Secretary of State for Wales on Monday in Prime Minister Theresa May's Tory cabinet.
Mr Bebb urged Mrs May to undertake a cross-party approach to Brexit and consider the Welsh Government's views.
Mr Bebb's Aberconwy majority was reduced from just under 4,000 to 635 in last week's general election.
He will continue as a government whip.
No replacement has been announced for the other junior Wales Office minister.
Lord Bourne has been appointed to the Northern Ireland Office as well as his existing role at the Department for Communities and Local Government.
Guto Bebb, the Conservative MP for Aberconwy, has been reappointed as a Wales Office minister.