The visitors were arguably the better side in the first half and comfortably survived after the break. Barcelona dominated possession but created far too few chances.
The Catalans remain the favourites in Group F after collecting eight points from their first four matches.
Barcelona predictably took control of the ball early, but the first real chance fell to the visitors. Gerard Pique nearly turned the ball into his own net after a sharp cross, but fortunately for the defender, Marc-Andre ter Stegen was there to make the save.
Pique made up for his mistake by finding Nelson Semedo with a great pass minutes later, but the full-back couldn't work the ball past goalkeeper Ondrej Kolar.
For all of their possession, Barcelona didn't create much danger, and the Camp Nou crowd soon started to voice its disapproval. Football blogger Warriors of Uruguay was not impressed with the action on offer:
Ousmane Dembele and Antoine Griezmann were invisible for long stretches of the first half. The latter hasn't been a smash hit since his move in the summer, and AS' Robbie Dunne wondered about his fit on the team:
Nicolae Stanciu had a half-chance to open the scoring shortly before the half-hour mark, but he had his shot blocked by a team-mate. On the other end of the pitch, Lionel Messi went closest for the Blaugrana, cutting inside before hitting the crossbar.
Messi also had a shot saved by Kolar and there was some late drama to end the half, with the linesman ruling out a Slavia goal for offside.
At half-time, AFP's Tom Allnutt weighed in on the action:
Messi had the chance to open the scoring early in the second half, but curled his free-kick from close range over the bar. Sergi Roberto went close shortly after, but Kolar was well-positioned to deal with his volley.
The VAR came into play on the hour mark, denying the hots the opener after Messi had played in Arturo Vidal. The linesman raised his flag, and the replay confirmed the Argentina international was offside by the tiniest of margins.
Ansu Fati made his way onto the pitch after 65 minutes, replacing Dembele, who was jeered by a section of the fans as he made his way off.
The change didn't improve Barcelona's play much, although the youngster did play in Messi with a clever pass, only for Kolar to make yet another good save.
Barcelona made a late push for a winner and found two more chances, but both Messi and Ivan Rakitic couldn't find any open team-mates in the box. Slavia did a fine job running out the clock, picking up their second point in four matches.
Barcelona host Celta Vigo in La Liga on Saturday. Slavia will be at home to Teplice in the Czech First League on Sunday.