The former Bantams player and Carlisle United manager will take time away from the role at Valley Parade and will have surgery.
Abbott says that the decision to step away was a difficult one but has put plans in place to ensure that the League One club continues to run smoothly in his absence.
"Having known about my condition for the past five to six weeks I have prepared a list of players for the manager and chairman in every position ahead of next season," Abbott told the club website.
"I take my role very seriously and am passionate about developing Bradford City on and off the field. It's my club. It may have been a tough season but recruitment is an ongoing process and actually it never stops, neither do I.
"Reluctantly I'll be taking some time away from the club but I'll be back. Rest assured I have planned everything in my absence from pre-season friendly fixtures, games for scouts to watch, players to observe and chase so we'll be well placed come the end of the season."