Cloud computing creates an interesting environment that enables people and establishments to accomplish numerous functions such as reachable storage space, use of business software, specialised or customised software and development of a convincing network platform. The information and Communications Technology (ICT) world witnessed and still witnessing the growth of a technology model named cloud computing with applications such as software as a service (SaaS), which emerged as a revolutionary paradigm through which organizations can optimize their ICT investment. SaaS is an innovation in which services and data are stored in massively accessible data centres in the cloud and can be retrieved through procedures online, appropriate for the obsolete traditional method where organisations develop commercial data centres, set up the software and are accountable for managing their IT infrastructure. This paper conducted a review on the vulnerabilities of Cloud Application Services (SaaS), critical challenges posed by the adoption and usage of cloud computing (SaaS) ascribed to possible attacks exploiting these vulnerabilities and proposes required security components to prevent the attacks and mitigate the risk of such exploitation, especially but not limited to the geographical location, Nigeria and developing countries in Africa.