1590s, "to make deaf," from deaf + -en (1). The earlier verb was simply deaf (mid-15c.). For "to become deaf, to grow deaf," Old English had adeafian (intransitive), which survived into Middle English as deave but then took on a transitive sense from mid-14c. and sank from use except in dialects (where it mostly has transitive and figurative senses), leaving English without an intransitive verb here.
1. This noise will deafen us all!
2. DEAFEN A sudden explosion deafened us for a moment.