A first Monaco goal for Elderson Echiejile gave the hosts the lead at the Stade Louis II, but Moukandjo's late strike denied them a third consecutive Ligue 1 win.
Reims threatened once before the opening goal as Mohamed Fofana headed wide at the far post.
Bernardo Silva, preferred to dropped £30m man Joao Moutinho in midfield, provided Echiejile with Monaco's breakthrough as he released the overlapping full-back to squeeze home from a tight angle.
The game went through a quiet spell before the hosts pushed for a second prior to the break, but Martial was again high with an effort from inside the box, while Geoffrey Kondogbia had a shot blocked.
There were more bright moments for Leonardo Jardim's side after the resumption of play as Valere Germain came close after being picked out by Elderson, and Ricardo Carvalho headed narrowly over from a corner.
While Traore and Moutinho came off the bench for the big-spending hosts, Moukandjo replaced former Liverpool striker David N'gog on 62 minutes and equalised with Reims's first shot on target.
He converted from inside the six-yard box at the end of a counter-attack led by fellow substitute Nicolas de Preville as Reims extended their unbeaten run to four games with a point which sends them 12th in the table.