The recently installed Roman Catholic archbishop will also greet tunnel workers during Friday morning's visit to the site in Chelsea.
The 100-ton machines are expected to start work in mid-May. Together the machines will cut two 7,100-foot tunnels through the hard rock underneath midtown Manhattan.
The No. 7 line subway extension is expected to open in 2013. City officials predict it will spur development of the far West Side.
The archbishop's visit coincides with the May 1 celebration of the feast of St. Joseph the Worker.