Jon Walters went closest to breaking the deadlock for Town but Blues had to settle for a point at a sun drenched Portman Road.
The Town midfielder was denied by a smart save from Chris Weale while the Foxes could have won it through former Blue Wayne Brown, who headed the best chance of the game over the bar early on.
A minute's applause reverberated around Portman Road before kick-off in honour of Sir Bobby Robson as the Town faithful paid their respects to a football legend.
Current Town boss Roy Keane made two changes to the side that lost at Coventry last week, David Wright replacing Alex Bruce and Colin Healy coming in for his debut and taking over from David Norris, who is out for four months with knee ligament damage.
Leicester started with the confidence that comes with two wins from two games and should have been ahead within three minutes, former Town defender Wayne Brown heading over after Blues had switched off at a free-kick.
Jon Stead couldn't get any power on his header as Brown struggled to deal with the ball inside the Foxes' box, Damien Delaney then firing well over from distance.
Lee Martin escaped Robbie Neilson and burst in on goal but couldn't beat Weale from the angle, Neilson then sending a 25 yarder wide at the other end.
Richard Wright dealt with Matty Fryatt's effort as Leicester threatened on the break, the Foxes enjoying an impressive record on their travels last season that helped them to the League One title.
Steve Howard failed to find the target with a gilt edged chance on 20 minutes, the striker left alone to volley Neilson's throw over the bar from six yards.
Town's best effort of the first-half came from Jon Walters, who forced Weale into a diving save low to his left.
Brown was in the right place to head clear from Martin's cross, with Lloyd Dyer finishing the half with a free-kick into the sidenetting after Gareth McAuley had fouled Howard, earning the former Leicester defender a yellow card.
Town made two changes at the break, Tamas Priskin coming on for his home debut and Connor Wickham joining him in a two man attack, with Stead and Healy making way.
Leicester started the second-half in lively fashion and Fryatt forced Wright into a save low to his right. Richie Wellens quickly joining McAuley in referee Phil Crossley's notebook for a foul on Martin.
Wickham didn't think twice when he picked up the ball from David Wright 35 yards out, blasting just over, while at the other end, Dany N'Guessan cut inside but with the same result.
Fryatt hooked his shot just wide after Howard had headed back into the box, Pim Balkestein then failing to find the target from the edge of the box. Weale saving from Walters, Wickham deflecting Wright's cross just wide.
Leicester introduced Martyn Waghorn and Andy King for N'Guessan and Fryatt midway through the half, Owen Garvan also joining the action for Martin.
Jaime Peters slid his shot past the near post as Town enjoyed a spell of possession around the Leicester box, with the Foxes making a final change with Nicky Adams replacing Dyer.
Howard almost grabbed the advantage for Leicester 10 minutes from the end, his header skimming inches wide of the far post from Neilson's throw, the Foxes' frontman yellow carded seconds later for a foul on Peters.
Waghorn followed soon after for timewasting, Weale likewise with five minutes left on the clock as the game ended goalless.
Town: R.Wright, D.Wright, McAuley, Balkestein, Delaney, Walters, Healy (Priskin 46), Peters, Trotter, Martin (Garvan 63), Stead (Wickham 46). Subs not used: Bruce, Colback, Supple, Smith. Booked: McAuley.
Leicester: Weale, Neilson, Brown, Hobbs, Berner, N'Guessan (King 63), Oakley, Wellens, Dyer (Adams 75), Fryatt (Waghorn 63), Howard. Subs not used: Morrison, Tunchev, Dickov, Logan. Booked: Wellens, Howard, Waghorn, Weale.
Att: 22,454
