The influence of radio frequency microwaves on the Coulomb blockade characteristics in small Josephson junctions was studied using a one-dimensional array of ten small Al tunnel junctions in the frequency range from 1 MHz to 1000 MHz. Coulomb blockade voltage ($V_{rm th}$) is diminished with increasing microwave power ($V_{rm ac}$), where the $V_{rm th}$-$V_{rm ac}$ plots for varied frequencies fall on a single curve. We observed and theoretically analyzed a magnetic field $dependent$ renormalization of the applied microwave power, in addition to a magnetic-field $independent$ renormalization effect explained using an effective circuit approach of the array. Due to its high sensitivity to microwave power, the array is well-suited for on-chip detection applications in low temperature environments.