FIFA did not give further details but African soccer's governing body (CAF) said at the time that Lamptey had wrongly awarded a penalty to the South Africans and suspended him for three months.
The life ban for Lamptey was recently upheld by the Swiss-based Court of Arbitration for Sport (CAS).
"The Bureau for the FIFA World Cup Qualifiers ordered a replay of the qualification match between South Africa and Senegal held on 12 November 2016," FIFA said in a statement on Wednesday.
"The match will be replayed within the November 2017 international window, with the exact date to be confirmed in due course.
"As stated in the FIFA World Cup regulations, this decision shall come into effect immediately but shall be subject to confirmation by the Organising Committee for FIFA Competitions at its next meeting, scheduled for 14 September," added the FIFA statement.
CAF had said that Lamptey was guilty of "poor performance" in the match and "awarded a wrong penalty for handball despite the fact that the ball never touched the hand of the player".
Thulani Hlatshwayo converted the penalty in the 42nd minute and Thulani Serero added another goal three minutes later.
Lamptey previously served a six-month ban, imposed by CAF, for wrongly awarding a goal during a CAF Champions League semi-final in 2010.
(Reporting by Simon Evans; Editing by Toby Davis)
