The Shrews arrived at the ground 30 minutes before kick off after a fire in the stadium, so unsurprisingly they started slowly.
In the fourth minute Scott Davies broke clean through the visitors defence, but his heavy touch passed the ball back to Luke Daniels.
Shrewsbury responded on nine minutes when Ben Davies drove down the left flank and crossed to Grant Holt. The striker has 24 goals in all competitions but failed to add to his tally, heading the simplest of chances wide from six yards.
Aldershot moved up a gear, and should have capitalised on their pressure.
On 18 minutes Jake Robinson picked up a loose ball on the edge of the area after the Shrews defence failed to clear. The Brighton loanee went for placement, curling the ball wide of the right post.
Both sides huffed and puffed in the second half and seemed content on sharing the points.
On 55 minutes the hapless Mikhael Jaimez-Ruiz almost gifted the visitors the lead when he fired his clearance into the back of David Worrall. Luckily for the goalkeeper the deflection bounced past his post.
On the hour mark Ben Davies broke free down the right flank and fed Holt who needed just the faintest of touches to score but was unable to apply the finish.
On 79 minutes Shrewsbury almost snatched an unlikely victory when Shane Sherriff unleashed a stinging volley from the edge of the penalty area.
Jaimez-Ruiz picked the flight of the ball late but produced a stunning reaction save to give Aldershot a share of the spoils.