The Sky Blues had the better of a tight contest and came closest to finding a winner when a 25-yard strike by Jacob Murphy hit the post after the break.
Gillingham had started brightly with Dominic Samuel wasting a good opening when he slipped at the vital moment.
Gael Bigirimana also went close with a curling shot for City, who dropped to 11th, nine points off the play-offs.
The Gills are now 10 points off top spot following Wigan's win over Shrewsbury, but they have a game in hand on the Latics and second-placed Burton.
Covnetry City boss Tony Mowbray told BBC Coventry & Warwickshire:
"I think late on we should have won that. It was alright, although for most of it was a pretty poor football match.
"We had a gameplan and it nearly paid off.  We nearly came away with a 1-0 victory but it wasn't to be."
Mid-table Coventry City earned a point from a drab match as Gillingham missed the chance to go third in League One.