The news continued the club's dismal week after Tuesday's confirmation that their 12-point Premiership deduction would remain following a failed appeal.
A day later, Portadown conceded two late goals to lose 4-3 against Crusaders in the League Cup.
"I believe the time is right to step away - I've done all I can to move the club forward," said McGibbon.
After serving an interim boss following long-serving Ronnie McFall's resignation in early March, former Manchester United defender McGibbon was appointed manager in late April.
However, six weeks later Portadown were handed a 12-point deduction for this season's Premiership after an Irish FA disciplinary committee ruled that they had paid player Peter McMahon even though he had been registered on amateur forms.
Portadown were already facing a transfer embargo in addition to being fined £5,000 because of a further registration breach involving Gary Twigg.
The Shamrock Park club were handed a total ban from all football related activity in late July for a failure to pay the £5,000 fine and their first scheduled league game of the season against Coleraine on 6 August was postponed.
Portadown appealed against both penalties but their pleas were rejected by an Irish FA appeal panel last Tuesday.
"As a former player both at youth team and first team level, I am devastated to see the current state of the club," added McGibbon.
"Recent events have had a demoralising effect on players, management and supporters alike.
"Despite player restrictions and ongoing administrative issues, I have been working hard with Vinny, the players and the rest of the management staff to improve fortunes on the pitch.
"However, I have found that my roles and responsibilities have been taken up more as a general manager than from a first team management perspective.
"Vinny and the rest of the backroom team have been terrific in helping with training whilst I have prioritised and dealt with other issues."
Crisis club Portadown are looking for a new manager after Pat McGibbon resigned on Friday evening.