Both teams put up a good fight in the game but failed to register a goal for the entire 90 minutes.
Enyimba have now garnered four points from two games, while Akwa United, who are winless this season have one point from two games.
In Group B, Abia Warriors maintained their unbeaten start courtesy of a 3-1 win against Bayelsa United at the Umuahia Township Stadium.
Kalu Nweke put the hosts in front on second minutes with an easy tap in.
The hosts doubled their advantage in the 65th minute through Bello Lukman, who slotted the ball home following an exquisite pocket pass from Henry Udezuka.
Lukman has now scored two goals in two league outings for Abia Warriors this season.
Henry Udezuka added the third three minutes from time.
At the New Jos Stadium, Lobi Stars pip Rangers 1-0 with Joseph Atule scoring the winner eight minutes from time.
In the day’s other game, Dakkada defeated Wikki Tourists 2-1.