Germany forward Linden, who was signed from Frankfurt, nodded in from a Kerys Harrop cross to salvage a point.
Melissa Fletcher had put the hosts ahead, meeting an Emma Follis cross to head home after the break.
Reading goalkeeper Mary Earps made a series of fine saves, but could do nothing to deny Linden on 73 minutes.
Reading Women: Earps, Jane, Hines, McGee, Follis (Allen 74), Bruton, Boho-Sayo (Jones 80), Davies, Perry, Fletcher (Ward 68), Rowe.
Substitutes not used: Sansom, Bartrip, Roche, Walkley
Birmingham City Ladies: Windell, Carter, Harrop, Ayisi (Scofield 57), Linden, Hegerberg, Stringer (Peplow 68), Lawley, Wellings,  Mannion, Berger.
Substitutes not used: Baggaley, Edwards, Shroder, Haines, Johnson
Attendance: 691
Referee: Ashvin Degnarain
Match ends, Reading Ladies 1, Birmingham City Ladies 1.
Second Half ends, Reading Ladies 1, Birmingham City Ladies 1.
Attempt missed. Isabelle Linden (Birmingham City Ladies) header from very close range misses to the left.
Attempt blocked. Connie Schofield (Birmingham City Ladies) left footed shot from outside the box is blocked.
Attempt blocked. Connie Schofield (Birmingham City Ladies) right footed shot from outside the box is blocked.
Melissa Lawley (Birmingham City Ladies) wins a free kick in the defensive half.
Foul by Remi Allen (Reading Ladies).
Isabelle Linden (Birmingham City Ladies) is shown the yellow card.
Kylie Davies (Reading Ladies) wins a free kick in the attacking half.
Foul by Isabelle Linden (Birmingham City Ladies).
Lauren Bruton (Reading Ladies) wins a free kick in the attacking half.
Foul by Chloe Peplow (Birmingham City Ladies).
Corner,  Birmingham City Ladies. Conceded by Kylie Davies.
Corner,  Birmingham City Ladies. Conceded by Mary Earps.
Attempt saved. Charlie Wellings (Birmingham City Ladies) header from the centre of the box is saved in the bottom right corner.
Foul by Nia Jones (Reading Ladies).
Jessica Carter (Birmingham City Ladies) wins a free kick in the attacking half.
Lauren Bruton (Reading Ladies) wins a free kick in the attacking half.
Foul by Kerys Harrop (Birmingham City Ladies).
Foul by Sophie Perry (Reading Ladies).
Melissa Lawley (Birmingham City Ladies) wins a free kick in the defensive half.
Substitution, Reading Ladies. Nia Jones replaces Jade.
Lauren Bruton (Reading Ladies) wins a free kick in the defensive half.
Foul by Connie Schofield (Birmingham City Ladies).
Substitution, Reading Ladies. Remi Allen replaces Emma Follis because of an injury.
Goal!  Reading Ladies 1, Birmingham City Ladies 1. Isabelle Linden (Birmingham City Ladies) header from the centre of the box to the bottom right corner. Assisted by Kerys Harrop.
Attempt missed. Rachel Rowe (Reading Ladies) right footed shot from outside the box misses to the right.
Attempt missed. Andrine Hegerberg (Birmingham City Ladies) left footed shot from outside the box is too high.
Attempt saved. Isabelle Linden (Birmingham City Ladies) right footed shot from the right side of the box is saved in the bottom left corner.
Substitution, Reading Ladies. Helen Ward replaces Melissa Fletcher.
Substitution, Birmingham City Ladies. Chloe Peplow replaces Abbey-Leigh Stringer.
Foul by Jade (Reading Ladies).
Jessica Carter (Birmingham City Ladies) wins a free kick in the defensive half.
Attempt missed. Abbey-Leigh Stringer (Birmingham City Ladies) right footed shot from the centre of the box is too high following a corner.
Attempt blocked. Isabelle Linden (Birmingham City Ladies) right footed shot from the right side of the box is blocked.
Corner,  Birmingham City Ladies. Conceded by Rebecca Jane.
Attempt missed. Connie Schofield (Birmingham City Ladies) left footed shot from outside the box is too high following a set piece situation.
Foul by Lauren Bruton (Reading Ladies).
Melissa Lawley (Birmingham City Ladies) wins a free kick in the defensive half.
Melissa Fletcher (Reading Ladies) is shown the yellow card for a bad foul.
Birmingham City's Isabelle Linden scored her first goal in English football to deny Reading their first Women's Super League One win.