Brendan Rodgers’ side, who currently sit third in the Premier League, failed to create many clear-cut chances on a frustrating evening in Prague.
Harvey Barnes came closest, when he was denied from close range in the first half, but the hosts put Leicester under some pressure after the break.
The return leg will be played at King Power Stadium on Thursday, 25 February.
When Marc Albrighton fired inches wide within seconds of kick-off, it looked like it could be a promising night for Leicester. But despite showing glimpses of creativity in the first half, they never really got going.
In-form Barnes, who has contributed to 11 goals in 23 league games so far this season, was played in by Youri Tielemans and raced through one-on-one with the goalkeeper only to poke it straight at his legs.
He was the most likely provider for Leicester – dragging another shot wide from a corner in the first half before almost setting up substitute Kelechi Iheanacho late on.
Slavia Prague full-back Alexander Bah and midfielder Nicolae Stanciu had half-chances for the hosts but Leicester goalkeeper Kasper Schmeichel was never truly troubled.
And when Rodgers took off key players Jamie Vardy and James Maddison after an hour, he looked resigned to settle for a draw away from home and a clean sheet, with the only regret being the yellow card shown to Iheanacho that rules him out of the next match.