After a creditable 0-0 at Burton, it was hoped that Neal Ardley's side would be able to give the promotion chasers a hard battle but it became even more difficult.
The Dons lost goalkeeper James Shea to a facial injury in the first half as Joe McDonnell came on to replace him.
The 20-year-old debutant could do nothing about Liam Lawrence's opener in first-half stoppage time as the Shrews took the lead.
Scott Vernon doubled the lead for the home side four minutes after the break, heading home a corner at the near post.
Wimbledon huffed and puffed but were unable to break down a Shrewsbury side who seemingly did not need to go above second gear.