Open Educational Resources (OERs) has entered the world of academia and has inspired innovation in education since 1990s, yet OERs awareness in higher education (HE) remains very low in Tanzania. Educators in Higher learning institutions (HLIs) in Sub-Saharan Africa are striving to provide effective learning experiences to address the needs of university students in crowded classes with limited printed resources. OERs currently hold great promise for instructing university students because unlike traditional curriculum materials, OERs content can be copied, used, adapted, adopted and re-shared for free. This paper presents findings obtained from the baseline study conducted at the State University of Zanzibar (SUZA) to explore the students’ OERs awareness. In the academic year 2014/2015, 352 out of 713 first year undergraduate students (randomly sampled) from three campuses participated in the study. Online questionnaire survey was employed and the data were analyzed. We first show that there is a serious gap in OER knowledge followed by a number of structural and contextual barriers. We further revealed that more than 40% of students are not exposed to OERs offerings. Overall the data revealed that the use of OER at university is low, however, there is potential for growth of OERs as many students have mobile and are using ICT for education. Most participants cited limited access, limited connectivity, and affordability to be significant barriers to wider adoption of OERs. There were also concerns about the limited ICT infrastructure at SUZA and the need to build the capacity of academics on OER integration.