Promotion-chasing Town were leading 1-0 thanks to a strike from top scorer James Collins.
But on 64 minutes the lights went out and an announcement asked fans to leave the East Stand. After a 20-minute wait, the game was called off.
A point would have lifted Shrewsbury into the top two of League Two.
But on a night when they could have gone second, Shrewsbury actually drop from third to fourth as a result of Crawley's victory at Bradford. With a busy Easter schedule ahead it will be interesting to see when the game is fitted into a busy fixture list.