Update 2021: shorter notation:
type arrMin1Str = [string, ...string[]]; // The minimum is 1 string.
OR
type arrMin2Strs = [string, string, ...string[]]; // The minimum is 2 strings.
OR
type arrMin3Strs = [string, string, string, ...string[]]; // The minimum is 3 strings.
OR …so on
This is just an addition to @KPD and @Steve Adams answers, since all specified types are the same.
This should be a valid syntax since TypeScript 3.0+ (2018).