Conor Chaplin gave the Blues the lead in the 22nd minute but Shaun Whalley levelled for Shrewsbury five minutes later to leave the scoreline 1-1 at half-time at Portman Road.
Fulham are being linked with a move for Town centre-half Tommy Smith, while Blackburn and Reading are also said to be showing interest in the 26-year-old.
Town boss Mick McCarthy felt his side were excellent during the second half despite conceding the goal which saw Barnet to a 1-0 pre-season friendly victory at The Hive. John Akinde netted from the penalty spot in the 68th minute.
Town boss Mick McCarthy was pleased to see most of his players get their first 45 minutes of football under their belts as the Blues beat Shelbourne 2-1 in their opening pre-season friendly of the summer at Tolka Park. Brett Pitman and Freddie Sears were on target for Town with Dylan Grimes pulling one back for the home side from the spot.