The draw leaves Masry second in Group D with six points, five behind leaders Zamalek, who have already secured their place in the next round with 11 points after defeating Black Bulls of Mozambique.
Black Bulls are fourth of the group with four points.
Masry will now face a decisive clash with Black Bulls at home on Sunday, 19 January, as they need to secure the victory to seal their passage to the next round.
Mohamed Hashem gave Masry an early lead in the 8th minute, but Ifeanyi Imehekwele equalized for Enyimba two minutes after the restart.
Masry's Mahmoud Hamada had a golden opportunity to secure all three points, but his penalty was saved.
Despite dominating possession and creating the better chances, the Egyptian side were unable to capitalize on their superiority.
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