The runner, in his 30s, was taken to hospital after crossing the line at the Madejski Stadium but could not be resuscitated.
A spokeswoman for the half marathon said it was "deeply upsetting and our thoughts are with his family and friends at this distressing time".
More than 16,000 people ran the 13.1-mile (21km) course through the town.
The runner, who has not been identified, had completed the course in two hours 30 minutes.
Emergency workers tried to revive him with a defibrillator after he collapsed and he was taken to hospital but could not be resuscitated.