We generated 274 SARS-CoV-2 genomes from samples collected during the early phase of the Kenyan pandemic. Phylogenetic analysis identified 8 global lineages and at least 76 independent SARS-CoV-2 introductions into Kenyan coast. The dominant B.1 lineage (European origin) accounted for 82.1% of the cases. Lineages A, B and B.4 were detected from screened individuals at the Kenya-Tanzania border or returning travellers but did not lead to established transmission. Though multiple lineages were introduced in coastal Kenya within three months following the initial confirmed case, none showed extensive local expansion other than cases characterised by lineage B.1, which accounted for 45 of the 76 introductions. We conclude that the international points of entry were important conduits of SARS-CoV-2 importations. We speculate that early public health responses prevented many introductions leading to established transmission, but nevertheless a few undetected introductions were sufficient to give rise to an established epidemic.