In order to get into this field you ideally need to be a civil engineer.
But like you say that you are a science graduate, you cant now get into civil engineering.
Certainly you can get into construction management. There are several Post Graduate Diplomas and Certificate level courses in construction/project management. Only Bachelor in Engineering/ Technology/ Architecture students are eligible for these courses. Some institutes conduct entrance examinations for admission into these courses. However some also enroll students on the basis of management entrance tests like CAT/XAT/MAT.
There are only few institutes in the country that offer courses in construction/project management. Some premier institutes are National Institute of Construction Management and Research (NICMAR), Pune; The Centre for Environmental Planning and Technology, Ahmedabad; Indian Institute of Technology, Madras; University of Roorkee, Roorkee and Anna University, Chennai. Besides Indira Gandhi National Open University, New Delhi also offers distance learning courses in construction/project management.
Hope this helps.