The Foxes' stalemate ensured they left the Eden Arena favourites to progress after the first leg of their last-32 tie.
Boss Brendan Rodgers has never reached the last 16 of the competition after four attempts with Liverpool and Celtic.
But after a draw in the Czech Republic the Foxes will be confident ahead of next week's second leg at the King Power Stadium.
Harvey Barnes was denied by Slavia goalkeeper Ondrej Kolar in the first half but the visitors struggled to maintain their threat after the break.
They needed Kasper Schmeichel to turn Nico Stanciu's drive over as the hosts were also left frustrated.
The Foxes started well as Marc Albrighton shot wide and James Maddison fired over inside the opening four minutes.
Nine minutes later Youri Tielemans' crossfield ball released Barnes ahead of Alexander Bah and the winger burst into the box only to be denied by Kolar from close range.
Yet it was the only serious chance the Foxes carved out in the first half at the Eden Arena.
The Czech champions created brief openings, with Bah heading the best of them wide at the far post, but they were restricted despite 14-goal top scorer Abdallah Sima's endeavour.
In a reflection of the half Leicester snatched at their other chances as Barnes hooked wide and had penalty claims waved away while Tielemans dragged wide just before the break.
They remained positive – especially with in-form Barnes' relentless desire to go forward – until losing their momentum after the break.
Slavia unsettled the Foxes, Schmeichel gathering Stanciu's free-kick, before the Romania international forced the goalkeeper to turn his 25-yard drive over after 58 minutes.
It was a marked difference from Leicester's first-half display where, while they were never dominant, there was always a degree of control.
The striker, though, was immediately booked after catching Jakub Hromada and will miss next week's second leg.
James Maddison came off for Hamza Choudhury 12 minutes later as Rodgers ensured Leicester held firm.